Practice moving the muscles in your face independently of each other. The trademark moving eyebrows that he uses in "You, me and Irene," to show differences between the personalities, needs lots of practice. Isolate the muscle and then concentrate on keeping the other features of your face immobile.
Set your teeth together and split your lips open as wide as you can. One of Jim's most recognizable expressions is his huge smile, which he uses in many of his movies, most notably "The Mask" and "Ace Ventura." It helps if you have a large mouth and a straight set of pearly whites just like the actor.
Watch celebrities and take notes of their trademark gestures or expressions. Jim Carrey started his stand up comedy routines with celebrity impersonations. Develop your eye for tell tale signs and then exaggerate them as much as possible.
Accompany your expressions with overdone exclamations or physical gestures. Carrey uses all these elements in his comedy as you can see in "Lemony Snickets," where he plays multiple roles and defines each of them with a complete set of characteristics. Define your role more by adding in complimentary attributes.
Begin as soon as you can and practice at every opportunity. Carrey was a performer as early as junior high when he did stand up routines in front of the school and this early start is responsible for some of his success. Hone in on your talents and stand in front of the mirror or an audience to gage your success.