A walkthru, using a hypothetical example of a Technomancer with 4s in every attribute.
1) Quantify how powerful a Sprite you want to try to get. The higher the Sprite's Level, the harder it is to get but the more powerful it is. A rule of thumb: a Sprite will be rolling twice its Level in all tasks, so for example if you know the target you want to your Sprite to effect is rolling 9 dice to defend itself from Matrix attacks, then you'll want to consider at least a Level 5 Sprite.
2) Make the test to acquire the Sprite. This is called Compiling, and see pg. 191. The TM rolls Tasking + Resonance versus the Sprite Level x2. In our example where the TM has 4s in every stat, and is trying to acquire a Level 5 Sprite, that's 8 dice vs 10 dice. Let's say that due to luck and/or Edge expenditure, the TM has 3 hits to the Sprite's 2. That's a success with 1 net hit, which means the Level 5 Sprite is successfully Compiled with 1 service.
3) The TM must deal with the blowback of Compiling the sprite, which is measured as Fading. The Sprite rolled 2 hits, which means the TM must resist 2 Fading damage. The TM rolls Willpower + Charisma, with each hit reducing the Fading by 1. In this case, the TM is rolling 8 dice again, and should probably be able to manage at least 2 hits. But if the TM is unlucky and/or unable to use Edge, the hits on the Fading test are deducted from the Sprite's hits on the Compiling test and the final result is damage that goes to your character. If that final number is equal to or lower than your Resonance value, it's Stun damage. If it's higher, it's Physical damage.
See also the sidebar in the upper left corner of pg 192 for a contextual walk-thru of this process.