The Thai elbow is almost un-useable in MMA....why? Simply because a good Thai elbow uses the very tip of the elbow and the UFC do not allow point of the elbow strikes (there elbows are forearm strikes)
Anyhow, some tips on elbow strikes:
Use the tip of the elbow, a harder area and smaller area - the elbow is designed as a cutting attack and not a concussive attack
the technique is deliverd through the rest of the body...NOT the arms. ie Side strike elbow uses the legs, hips and shoulders...an uppercut elbow uses the legs (as does a cirlcing downwards strike)
If you can elbow me....I can elbow you...therfore ensure that your free arm is protecting your head (especially the temple)
Always throw through the target
If you are using the pads, aim to just touch the pad...a forearm smash sounds better, but the grazing slice of an elbow on the pad....will result in an elbow that slices skin!
Thats all I can think of for the moment...maybe more later....on knees (Kao), clinch work and front kicks (Teap)