The Hugo awards are a part of the Worldcon, nominated and voted on by members of the Worldcon. Anyone can be a member of the current Worldcon by paying a membership fee. Supporting membership usually costs $40. That doesn't get you physical access to the con itself, attending membership is a lot more.
Joining the Worldcon makes you a member of the World Science Fiction Society (WSFS) for that year. As part of that membership you get nominating and voting rights for the Hugos including the right to nominate the next year but not vote. If you want to vote next year (that con will be in Kansas City in 2016) you need to pay for a supporting or attending membership for that specific convention.
I was a member of the 2014 Worldcon, nominated and voted that year and nominated this year but I couldn't vote this year since I didn't join Sasquan.
As I understand it a lot of people joined Sasquan as supporting members after the nominations closed simply to vote for the Hugos, generally opposing the slate nominees. They couldn't change the nomination lists but they could vote against the slate nominees. In the end the opposition was strong enough that most slate nominees ended up below No Award (or as David Gerrold calls it "Noah Ward").