Base Game
Take the time to learn the Base Game before you add in the Escalation expansion.
Pick either Warfare of Colonise for taking control of planets, don't try to use both.
Use the Research Action to remove the cards you don't plan on using. If you ever discard a card at the end of your round, ask yourself if you even want it in your deck.
Survey early to find planets which complement each other.
Try to get 3 planets of the same kind and push for the level 3 technology (7 research icons). These technologies give you game breaking abilities.
Remember that the planets don't have the level 1 technology that should match with them (Fertile does not have Improved Colonise, Advanced does not have Advanced Research and Metallic does not have Advanced Warfare)
Planets with a Colony symbol are a permanent discount to all colonisation costs instead of an extra icon when the role is chosen.
Planets which increase hand size will give you a lot more options each turn.
Keep an eye on how many cards are left in each role; if you're ahead consider taking a less efficient role to finish the game faster.
Escalation Expansion
Annex can really mess with colonisers.
You can buy research with fighters, destroyers and battlecruisers. If you Warfare, you can get game end tech without needing to lead Research roles.
Diverse Planets are now an option, especially with Oversight Committee consider pushing for one-of-each
Tips from the Pros
SMoslim
This is a Victory Point game the main source of VP's are your roles. You are allowed only one necessary 0 VP role, the one when you get your first tech. Next you should always get points in your roles. The main method to do that is to go for survey each time you cannot get points otherwise, especially in the beginning. A lot of beginners waist time in getting multiple level 1 tech that is useless because it is not worth the role you pay for them. You can however get them if you are following, not leading.
A tip I learned from analysing the top player is at the very beginning of the game; if you have first turn and you choose the Survey role, do not use any of your Survey cards. Keep them so you can use them to follow your opponent's Survey role.
If you get an Advanced Planet with a Research symbol early, consider skipping getting a Level 1 tech and get your fourth Research symbol from exchanging Politics for Research. This should be especially true if the Advanced world only needs 3 colonies to Settle.
In Escalation, Warfare is a big risk/big reward strategy. Most top players avoid it because of the risk. Skilled players can mix Warfare and Colonize mid game, but a player needs very specific circumstances and skills to make this work, so I do no advise this strategy for beginners. I would only go for Warfare in Escalation if I start with a metallic planet, and I Survey'd a metallic planet that only needs 4 fighters to attack, and preferably with a warfare symbol.
Not all tech cards are created equal, some of them are really powerful and should always be picked if they're available. Pay attention to what the top players choose. As your experience grows, and you can start paying attention to what your opponent is going for, you may get a less optimal technology just to prevent your opponent from getting it, since it fits perfectly into their strategy.
The Eminent Domain community on BGA is small, so it might be subject to "group think". Once you have became a strong player, you need to start experimenting with different strategies. Pay attention to what other players do that is unusual. Even when I thought I was an expert, I learned a lot from weaker players that were using unusual strategies.
I see a lot of players getting stuck in low levels even though they played a lot of games. The main reason, I believe, is because they never change their playing style and always do what they are used to. I am now a master, and I still think about a few strategies in the opening phases of the game that I figured weren't that optimal. So, you need to always keep evolving. I also asked some top players about the different tech cards and their strategies, however they never used them. That's a big mistake since it limits your growth, and although those players are great, they hit the limit of the potential of their limited strategies.
The main reason is one of two; they play on auto mode so they don't get out of their comfort zone. Or, they don't want to risk experimenting because losing comes at a great punishment, which I, personally, understand. The main solution to this is to play lots of Scenario games since they force new strategies on you while you are still a Good or Strong player since losing isn't that big of a deal that those levels. Now that I'm at a master ranking, losing any game absolutely destroys my ELO rating.
If you are really serious about the game, you need to start analysing high level player games and critique their decisions and compare them to yours. However, don't follow these games blindly, high level players aren't perfect, and also they don't always tale the game super seriously, and sometimes make a worse decision because it us more fun.
One of the most successful strategies that I use now is the Heavy Survey/Remove Cards opening strategy. I use this strategy because during a game, sometimes you get the perfect colonize hand but no Face Down planets, or more colonize cards than needed for the planets you have, so you are forced to play a suboptimal role. You never have this problem if you have an abundance of Face Down planets, so get a lot of planets in the early game so you can always have optimal turns and a lot of options to where you want to take the game according to your circumstance. When I first discovered this strategy, I quickly found it has a huge flaw, it fills your deck with Survey cards that are, generally, useless in the mid to late game. So, the Heavy Remove cards from the game strategy is needed as well. You need to keep removing those Survey cards from your deck, using the Research action, to keep your deck compact.
Another strategy that comes with this one. Is that you try to get at least one follow. Either by following Survey or Colonise. To that you need to keep your hand prepared for those. Following is main source of extra points in high level games. To have the ability to follow you need to keep checking your opponents discard pile so you can predict their next move. To do that you might need, from time to time, to use the wait option before the clean up phase to see if your opponents follows you. Just don't be the guy that use it all the time, especially in turn based games. I encountered a few of those players and it just slows down the game a lot for no reason.
Deck balance: a lot of rookies and some times top players go for heavy warfare or heavy survey without paying attention to their deck balance. Although it seems perfect at the start, they later start getting a lot of cards they don't need, or take roles they don't want to take, and it only gets worse and removing cards from your deck mid game is really suboptimal. So you need to avoid it. Unless you are using Oversight Commitee tech card, which is not as bad. Your deck needs to always be balanced so don't mess it up at the opening stage.
Discard pile: as previously said, pay attention to your opponents discard pile to predict if he is going to follow you or what is he going to play next turn.but another very important discard pile is the planets discard pile. When you became a strong player you should know all the planets of the game. so use the discard pile to predict what you might get. Although you cannot see the cards in the planets deck you can have perfect information just by looking at cards in colonies and the discard pile. Some times you give up on your perfect role just to play or follow a surveil role to get the top Planet because it is worth it for you or too good to let your opponent get it.
Bad tech cards are extremely powerful in some strategies: if you are going for a strategy double down on it in the tech cards have your entire deck go for it instead of having a diversified strat. It might seem simple as a tip but no very few players go for this because they are swayed buy the shiny good tech card. Because they are used to choosing it. Especially that this advice cannot always be used to the fullest since it is circumstance-specific. The real tip hiding behind this obvious one is always pay attention to your go-to moves yes they are the best in 90% of the times but not in 100% of them and this is why a lot of players never played some tech cards because they missed the opportunity to use them when the rare circumstance to use them optimally comes up.
Your action: most average to strong players don't understand how important this one is because roles are the source of points and the optimal action is most of the time obvious. But what they don't realise is that the action should be prepared. In the previous turn so you are not forced to an action.
One of the worst actions is the draw action it simply give you 0 point. It is only really useful when you are in a race against your opponent to get a tech card first. Or to have a really big role. But it's a really big one not to complete a normal one. Because when used to accomplish a big role it means
it made you play 2 roles in 1 and that is not a common situation. By the way getting a lvl 3 tech card isn't a big role that is just a normal role. I mean by big a 1.5 to 2 roles in one. In other terms wining points. Another wast of an action is the remove cards from hand one once you are no longer in the opening phase.
So you only have as a good action the suttel/attack or a tech that doesn't what a role doses or win points. Otherwise you are wasting an action.
This tip however is top tier one don't pay attention to it if you are an average player because it needs high lvl hand management. Otherwise your action is foced any way.
Deck cycle:
Much more tips to come this just the generalities. I'm tired now. If you are a native English speaker you might need to rephrase an reorganize most of this. If you find a tip not clear or if you don't agree with it. Tell me so I clarify or have a discussion so we converge or agree to disagree