Hi!
As Jon said, only ink comes off the transfer. Lift off the paper and you are done.
You may need to play around with pressing time and pressure as the results may vary depending on texture and thickness of the fabric; thikness and quality of paper and type of inks.
I.e. - thicker paper can leave an impression of the transfer on a t-shirts; uncut paper may add unwanted shine to the fabric; too high temperature may "yellow" a shirt and alter transfer colours...
After some trial and error you will find perfect settings for your combination of equipment, consumables and sub-strates that will get you perfect results.
Your goal is to get most of the dye off the transfer and into the fabric without leaving press marks/shine.
I'm trimming my transfers unless the order is quite big - I believe it looks better.
There are different fabrics for sublimating, but you will need at least 65% polyester for good results.
If you have satin or microfibre type of fabric - trimming is a good idea as sometimes the fabric tends to shine when pressed.
If you are pressing t-shirts that look and feel like cotton (follow Dye-Sublimation Info. link on the left to read about Vapor Apparel) - shine/press marks are not much of an issue.
Good luck with your venture!