There is no one specific method of physically taking the wrinkles out of a liner.  It’s really a matter of what works best for you.  Though there are really only 3 methods of when to take out the wrinkles.

1. Liner is in the pool and just sitting there - 
• There are times when a liner is put in a pool and it fits almost perfect with only minor wrinkles which "pull themselves out" when the weight of the water is applied and the liner stretches.
2. Liner is in the pool and a vacuum is used to suck the air out - 
   • Using a vacuum suck the air out from behind the liner. Be sure to seal with duct tape any openings around the pool that would prevent a good vacuum seal.   As the liner gets pulled back against the wall and floors you will be able to see how the liner will ‘lay down’. 
     It is at this point which the wrinkles can be worked out by spreading the liner in small increments in any number of different directions depending upon how the wrinkle lies and the height of the wrinkle.  Some wrinkles need to be slowly taken down over the course of a few feet of moving the wrinkle away and slowly making the wrinkle smaller and smaller until it disappears. 
     Once the wrinkles are out of the liner; leave the vacuum on until the pool has at least 12” of water in it.  This will allow the weight of the water to hold the liner in place when the vacuum is taken off of the liner.
3. Liner is in the pool and pool is filling with water - 
• Of the 3 methods, this can be the most difficult. It can be difficult because even an inch of water makes it very difficult to move the liner and slowly spread it out as described in step two above.
4. This is an unwritten fourth method which is to do both #2 and #3 above at the same time.  This process is really only for the pros because if you’re not quick about it the liner may get to much water on in and then you can’t move the liner any more.