Attending conferences is an important part of graduate education. There is much to learn from the presentations and short courses. PhD students should give one or more talks on their research at professional conferences and Master's students can benefit from this as well.
The American Mathematical Society has a calender of up coming conferences.
http://www.ams.org/meetings/calendar/mathcal
The AMS also sponsors its own conferences. There are regular regional meetings, a national meeting each January cosponsored with the MAA that includes a jobs fair, and international meetings. Meeting are organized into Special Sessions. Your advisor can help you find a session that might be a good fit for you. If none are you can still apply to give a contributed talk.
http://www.ams.org/meetings/meetings
The Mathematical Association of America focuses of teaching at the undergraduate level. It has regional meetings and sponsors a Math Fest each August.
SIAM is the Society for Industrial and Applied Mathematics.
ASA is the American Statistical Association.
http://www.amstat.org/meetings/index.cfm
If you are interested in community college teaching check out the American Mathematical Association of Two Year Colleges. They also have regular meetings.
If any of the links have gone bad, let us know, but you should be able to search for the correct site.