Wash your hands and wet the vaginal opening and the vagina itself with some saliva, making insertion easier.
Unwrap the tampon and pull the string to see if it is well attached.
Spread your legs (squatting or with one foot on the bed or toilet), pull your lips apart and push the tampon in your vagina with your index finger until it won’t go any deeper. Your vagina slants backwards. If you don’t know the angle, then explore your vagina with your finger first, so you’ll know in which direction you have to push the tampon.
You have to relax your PC-muscles, otherwise it’s painful or impossible to insert a tampon (see: vaginismus).
It’s in place if you don’t feel it anymore. If you still feel it you have too push it in deeper.
Never forget to take your last tampon out when your period is over!