When it comes to performing oral sex on someone with a vagina, how you do it depends on the person and what they find pleasurable. That involves the two of you communicating before, after, and during that activity and being willing to experiment a little. Often oral sex focuses on the outer parts of the genitals, mostly because the average human tongue isn't really long enough to do much if it's inserted into the vaginal canal. You can find out a bunch more on oral sex here: Mouthing Off on Oral Sex
Oral sex is often considered to have a lower chance of STI transmission than things like vaginal sex, but when a person is on their period that risk increases because there is contact with blood. You can read more about that here: http://www.scarleteen.com/article/advic ... rual_blood
. But, the simplest way to avoid transmission of STIs during oral sex on a vagina is to use a dental dam, which you can learn more about here: All the Barriers! All the Time!
. If you use a dental dam, you can have oral sex at any time you both want it.
In terms of keeping clean, the vagina is actually self-cleaning, although it's also recommended that people wash the outside gently with warm water. However, it isn't really on you to teach a partner how to do that; it's her body, and odds are she's figured out how to care for it just fine.