Before I went to the mikvah my rabbi emailed instructions to me. Here’s what I was told by my rabbi:
The mikvah is at Congregation Beth Jacob on Park Blvd (in Oakland). You ring the front door, and I will meet you in the lobby. The first step is meeting with the three rabbis for the beit din. You need to bring a $50 check made out to Congregation Beth Jacob to pay for use of the mikvah.
At the Beit Din, the three rabbis ask you questions. These are not fact-based questions but questions about what you like about Judaism, what you are doing currently in terms of Jewish observance, what Jewish holiday is meaningful to you, what Jewish books you are reading, connection to Israel. These are some examples, but they can ask you whatever they want. Often they ask you about things you wrote in your personal statement. This takes 10-15 minutes.
After your interview, and acceptance (I am 99.9% sure you will be accepted)*, you go into the mikvah. Wear no jewelry or makeup. You undress in the mikvah room, and the rabbis are in the next room. When you're ready to go in the water, you go in and call out "ready." For men a male rabbi will go in, and for women a female rabbi will go into the mikvah to supervise the immersion. The other rabbis from the beit din will wait outside within hearing range.
Here is the actual procedure inside the mikvah:
You go under the water three times. Go all the way, so the water covers your entire body, and recite the following blessing. If you don't have it memorized you can repeat after us.
Go under the first time and this is the blessing.
Baruch Ata Adonai Eloheinu Melech ha'olam asher kideshanu bemitzvotav vetzivanu al hatevila.
You then dunk a second time and recite the following blessing.
Baruch Ata Adonai Eloheinu Melech ha'olam shehecheyanu vekiamanu vehigianu lazman hazeh.
You then dunk a third time and recite the Shema.
Shema Yisrael Adonai Eloheinu Adonai echad.
The final part of your conversion comes at synagogue, where we do a ceremony where you hold the Torah and we "name" you publicly.
*Of course, no one can guarantee you will be accepted but your rabbi will not take you before a beit din if he or she is not confident that you are ready.