Look at the tampon....you'll see it seems to have two parts to it. they'll slide together when you push one against the other, and that'll position the cotton tampon inside when it's all said and done with.
Hold it between thumb and middle finger on the base of the tampon where the little grips are (usually there are little grips or a ridge). Easier if you part yourself with your left hand and hold the tampon with your right hand, if you're right hand dominant. Holding it this way, like a dart, keeping your pointer finger free, Insert the tampon until your thumb and middle finger are up against you, easiest way is to aim it to the small of your back. Relax down there....don't tense! it won't hurt! Once you insert it to the point where your fingers are touching yourself, use your pointer finger on that same hand to just "push in the plunger!"
Extract the used tampon bits. Never leave the tampon in for an extended length of time. Change them every 4-6 hours regardless of if they're saturated or not. If not it'll smell horrible, and could give you infection if left up in there too long
Slide entire tampon angled to the back, (not straight up) until the applicator is no longer visible.( for the first time, it may be helpful to squat, and use a mirror.) Gently grab hold of the applicator and pull it out. Tampon will remain. The string will remain visible. Practice on one before you insert to see how it works.