They are not very particular about mates. They will generally mate at certain times of the year but don't seem to be choosy about the partner. We don't know yet what times of year this happens. They are born with adult organs, and are ready to breed immediately. They are most likely to pick someone close to their own size.
More breeding seems to happen at certain times of year.
The male's terminal region will clasp onto the female's and he will protrude his genitalia into the female and inseminate her. About a year. A long time. Some sources say 270 days. The mother eel will get really wide.