Once you have your menstrual cup - it's best to do a little research to ensure you get the best brand to suit your body and needs, also be sure to get the correct size - remember that for some women it can take a little practice to learn to use a menstrual cup correctly so be paitent when first attempting to insert your cup.
Menstrual cups can be worn before menstruation, however at first it's best to attempt to insert during menstruation as blood gives more lubrication and your cervix will be in the position it will be in during menstruation. If worried about mess try inserting in the shower - it's best to try using cups in the bathroom where you have privacy and can clean-up.
Make sure you know where your vaginal opening is located (check online sites such as Scarleteen if unsure), it helps when inserting menstrual cups for you to know your anatomy well and be comfortable with vaginal penetration - this makes it easier and more comfortable. It also helps to check your cervix, the opening to your uterus located at the top of your vaginal canal that feels like a firm ball, you need to position your cup under your cervix - if your cervix is too high up to feel then chances are your cervix position won't be a problem.
Wash your hands well before insertion, also wash your cup if this is your first time using it - just use soap and water, but be sure to rinse well. Get yourself into a comfortable position and relax - if you're tense vaginal muscles will tense, this makes vaginal walls clench together so it is more difficult to insert anything vaginally.
When ready fold your cup - there are different folding methods, your cups instructions should show you at least one way to fold your cup but also look online for more folding techniques. With your other hand hold open your labia for easier access to the vaginal opening and when ready insert the cup while keeping it folded. Insert the cup as far as possible aiming towards the small of your back - once fully inserted allow it to pop open.
Once open and in place check to make sure it is fully open by running a finger around the cup, or turn it to both check it's open and create a seal to prevent leaking. Once in place it can be worn for up to 12 hours without any health risk or leaking, unless your flow is very heavy.
If you have any problems try asking for help on support communities such as http://www.menstrual-cups.livejournal.com