Evolving is a destructive method of acquiring new suits. Each unit has anywhere between one and four evolution paths. The only requirement for evolution is having a mobile suit sufficiently leveled. For example the Gundam can evolve into the Gundam Ground Type, G-3 Gundam, Gundam Unit 4, or Full Armor Gundam. The minimum level for each evolution is 2, 3, 4, and 5 respectively.
To evolve a unit, make sure it is sufficiently leveled for the evolution that you want to perform. From the Operation Room, go to the crew set up page (first option under exit). From the crew set up page, go to the unit page (second option). From the unit page, go to the second option (with a picture of one MS with three paths to other MSs. From there, choose the unit you want to evolve, when you go into the evolution menu, pick the unit that you want to evolve into, and you're done.