What is the process of getting married in Islam? The Muslim woman and I both converted to Islam and our families are not Muslim and we have no religious friends. Who do we talk to in order to get married?
Congratulations! I am happy to hear that you found each other.
It is permissible for you to recite the marriage contract yourselves. However, it is often nice to have a third party do it for you. I recommend that you call or e-mail a mosque (if there is not one near you, then one further away) and ask them to assist in conducting the marriage.
It is not unheard of for a religious marriage to be performed during a community gathering (such as Du'a Kumayl or a celebration) at a mosque, and this might be a good choice if you do not have Muslim religious friends, so that others can share in the occasion. You can always have another celebration later for other friends/family.
Best wishes!