Bacterial conjugation involves a RecA independent transfer of a single strand of DNA from doner to recipiant, generally via a sex pilus. The F plasmid is the best characterised example of this, but other plasmids are also capable of conjugation. In order for conjugation to be possible, two things must be present - a mechanism for the transfer of the DNA (the tra region on the F plasmid) and somewhere for the plasmid to be nicked and transfer to initiate (the OriT region on the F plasmid). There is no requirement for both of these to be on the same plasmid, although in the case of F they are.

Carrying the F plasmid causes the host bacterium to express the tra genes, one of which (traA) causes assembly of a sex pilus on the outside of the bacterium. If this pilus comes into contact with a bacterium not carrying the F plasmid (the traS and traT genes cause production of coat proteins that prevent sex pili from attaching), the two bacteria are drawn together and a pore opened between them. The OriT region of the F plasmid is nicked and rolling circle replication used to displace one strand. The displaced strand is guided through the pore by other tra genes and transferred to the recipient. Once there, the ends of the single strand are ligated and a new strand produced to bring it back to the double stranded state.

Conjugation is not limited to plasmids. The F plasmid is capable of recombining itself into the bacterial chromosome. Once there, the chromosome itself can be transferred. Usually the bacteria will drift apart before the entire chromosome can be transferred (conjugation is fairly slow. This is also true when it occurs in language classes. A-ha ha ha. Sorry.), so you can get some idea of how far apart two markers are by looking at the frequencies of co-conjugation. If a chromosome is copied, the high degree of homology with the recipient chromosome means that recombination is quite likely.

The idea of F+ and F- being analagous to male and female is only accurate if you don't object to the fact that in this analogy, women who consent to sex turn into men afterwards. Being F+ is not necessarily advantageous - the extra coat proteins produced make the bacterium in question more susceptible to bacteriophage infection, which is probably why F plasmids are not ubiquitous.