Do as few missions and assignments as possible until your search for information on Saren points you to the Med Clinic in the Ward. This occurs after you leave the Normandy for the first time, talk with Udina and the captain, then travel to Chora's Den.
When you arrive at the Med Clinic, there will be a battle and after that you choose to let Garrus into your party. Keep him in your party throughout all missions and assignments. For optimal effect, choose a character that is stronger in assault or casting depending on your character class. Garrus is strong in electronics, so I don't recommend choosing Tali, the quarian.
For missions see http://masseffect.wikia.com/wiki/Missions
. For assignments, see http://masseffect.wikia.com/wiki/Assignments
You need to do all the missions. While most of these open up automatically throughout the story line, there is one tricky one that you have to hunt for first: Novario: Quarantine (http://masseffect.wikia.com/wiki/Mass_Effect_Guide#Rift_Stat...
). To get this, find Dr. Zen Cohen in the medical bay at Rift Station on Novaria and talk to him about a cure. Do this mission.
You'll need to complete around 40-45 assignments with Garrus in your party. If you fly through the missions, make a game save right before leaving the Citadel for Ilos and play a bunch of assignments to be sure. Once you leave for Ilos you're pretty much stuck with finishing the main story line. With the game save before leaving for Ilos, you can at least reload it and do more assignments if you decide to finish the campain. Just don't overwrite it accidentally or you'll have to start a new play through.