Burglary missions are available from the beginning of the game and requires a Black Boxville in order to start it. You can find one of these next to the apartments across the street from the gym in Los Santos. This mission has a strict requirement, which is that it can only be done between 20:00 and 6:00 on the in-game clock.
Once you find a Black Boxville, press the right analog stick in on the Playstation 2 and Xbox versions, and the 2 key on the PC version. When you start, you will need to find a house to break into, which are conveniently marked with a yellow arrow outside of the front door. After going inside, you will need to sneak around to find objects of value, such as stereos, VCRs and televisions. Note that there is a meter that fills up as you cause noise and if it fills up all the way, you have 10 seconds to get out of the house before the police are alerted.
When you find something to steal, press Triangle (PS2), Y (Xbox) or the F key (PC) to pick it up. Once you do, you cannot sneak around anymore and must move at normal speed, which means the alert meter will fill up. Get outside and place the stolen item inside of the van. The alert meter empties once you go outside, so you're free to go back inside.
The Burglary mission ends when the timer reaches 6:00 on the in-game clock, but the loot in your truck isn't counted towards your overall total. Once you get the loot in your truck, you will need to drive it to the lockup to drop it off. You need to get a total of $10,000 across all Burglary missions to make it count as finished, not just $10,000 in one run.
