This is a suggestion that has gone over well for a few people I have told it to, so I figured I would share it here as well. Those who hit the game running or have been in the beta since 1987 need not apply.
One of the best ways to tackle a strategy game, and thankfully Sins supports features out of the box, is to watch a recorded game. Keep in mind that the computer AI is not the end all be all of greatest ideas ever and should be followed exactly, but it does help build some core ideas to try that you may not have thought of or noticed on your own.
Try playing a couple games with various amounts of computer players, various races, various difficulties and various map sizes. Don't worry too much about how you do as a player, but you are playing so you might as well play and have some fun. If you want you can play the game to the bitter end (or if you manage to sweet victory) but the first 10-15 minutes should be enough to get some ideas, but there is a lot to learn in the mid and late parts of the game.
Once you are finished go back and watch the game. You can review the manual (also available as manual.pdf in the folder the game is installed in, if you downloaded.) for more details on the recording and watching options.
A couple key things, however, is to keep in mind that the Pause/Break key will pause and unpause the game. Change who you are currently "watching" by clicking in the top-right corner, which will cycle through the players on the map. You can also switch the speed of playback and whether or not you can see the entire map or just what the current player has discovered.
Pause frequently in the first few minutes and pay attention to what is going on. Is the computer focusing on building ships? Research? Exploring? A bit of all of the above? Hopefully watching the various races, difficulty levels and even different maps will give you ideas of your own to try. It is also fun to see how you were doing 5 minutes in the game compared to your opponents. 5 minutes in and they already have 4 expansions setup and you are barely working on your second? Don't be suprised at how slow (or who knows how fast) you are compared.
There are also game replays that can be downloaded from the Downloads section that can show real players (who will always try and do crazy things that the computer never will) that are good to watch before you make the jump online playing with other real people and being destroyed. There are only a handful now, but hopefully people will contribute many for new players to watch and learn.
At the end of the day don't be affraid to try things even if they seem silly or a bad idea. Want to build nothing but scouts and run around everywhere? Go for it! The wealth of experience and knowledge you will gain just from trying even radical ideas may surprise you. The worst thing you could do, in my opinion, is become a slave to the same old strategy that you do every single match and never branch out trying different ways to play. If you tend to always focus on defense give a heavily aggressive offense a shot, and vice versa and back and forth.
Hope this is some useful information for anyone still a little weary after watching the tutorials and still cutting their teeth trying to find other things to try and ways to play.