I was just wondering how often these elections are held?
It can be at any frequency--it depends upon demand. If the current mods cannot keep up with the site, then more mods are elected. See Are sites limited to a maximum of one moderator election per year? as well (Thanks, Tim!)
Does the current moderator(s) stay until they don't want to do it anymore or is there a set period of time they are given the job for?
It's a permanent position, but entirely voluntary. Also, if you are absent for six months, your modship is taken away (it seems easy to get back, though).
From the December 2011 moderator newsletter:
Absentee Moderator Policy
We are in the process of implementing a policy for “absentee moderators” —
Any moderator who is not active on the site for a period of six months is subject to removal of their moderator abilities.
Moderatorship is an elected position, so if an absentee moderator returns to the site, they may be eligible for reinstatement. We understand that sometimes life happens: projects come up at work, other obligations take priority. If you need to take an extended leave of absence, just let us know and we will make the necessary accommodations. This policy is simply a way to help us better determine where additional help may be needed.