Import a Mass Effect 2 Character
If you have played Mass Effect 2 you can import a character from it. If you played on the PC it should happen automatically, or locate the save files that you want to use and put them in your documents folder similar to the way that the mass effect 3 folders look like. There is a very comprehensive guide on a site that will also provide you with Mass Effect 2 save files for the PC with various ways of having played the previous games: http://www.masseffect2saves.com/
If you import a character you start on the level of the imported character. This gave me around 50 skill points to spend which is very helpful to make the combat a little easier.
Focus on a Main Power
Each class has powers that it is particularly good at. For a summary of these go to my guide to the different classes here. Be sure to level up your main ability as quickly as possible. Look for the power upgrades that affect how many enemies are hit and how fast it recharges, which includes adding bonuses to weapon weight.
At the same time you will want to make sure you level up your standard class buff powers that increase shield, health and power damage etc. This is secondary as the main power boosts for them come from leveling the ability itself.
Don’t Waste Skill Points
You won’t have enough skill points to level each power to the top. Be careful in choosing whether or not you actually want an upgrade, especially with the later options some of which I found very useless which allowed me to save many skill points. In general look for power upgrades that have a major effect on area damage and recharge speed. Don’t bother with the power buffs that make you have a chance of not triggering the cool down because consistency is very important in your gameplay.
Often times some skills are under appreciated and overlooked. The first level of any power only costs one skill point, so every power is worth trying out unless you know what it does. This is why I also suggest putting your first play through not on Insanity, unless you find that combat is too easy. Especially when I was playing on normal the combat was boring and heavyly one sided, now I’m playing on Insanity because the Vanguard is very powerful. You can find a guide that helps you through Mass Effect 3 on Insanity here.