Important things:
* You want to make sure to have Long Range Radar in your base(s).
* You can give soldiers weapons to take advantage of their skills (e.g., guys with high Stamina and Strength, and at least decent Firing Accuracy make the best heavy gunners).
* Use proper squad level tactics to provide cover as you advance (and always check your corners).
* Always be researching, as completing research of alien items allows you to use them!
* Laser Pistols are a nice easy way to make money (build for $8k, sell for $23k, iirc), and they are a huge improvement over "standard" rifles.
* Wounded soldiers can be sold, however, they also have most likely made improvements in their stats. The Soldiers screen gives you the details on that.
* Use the Graphs option in the GeoScape to see where alien activity is happening so you can send interceptors on patrols in that area to find ships faster.
There are some other things, but most of them are easily discovered through playing the game. Personally, I add some letter codes to the soldiers names so I know what skills they are best at without having to check their stats all the time.
Also, Google for "The Legend of Patrick Stewart" for a nice example of how the games can play out.
