To be honest, it's fairly easy, and is always a good way to get whatever issue you care about out there, so people know what part of the world you'd like to change today.
Pretty much absolutely anything; from more books in the library to stopping climate change, almost anything qualifies! If you need any clarification, speak to one of the Union officers or staff.
This is the legwork, but it's not that bad, really. All you have to do is go to the General Office (ground floor of the Students' Union on Oxford Road) and get a General Meeting Motion form (or you can download the forms below). You don't have to tell them what it's about, just be polite, have your student card ready and it shouldn't be a problem. Don't forget to bring a friend, though, as all motions need proposers and seconders.
Now fill out the blurb and get 30 signatures to support you. Probably best to write the motion first, so people know what they're signing! It's always good to hit the Union bar or Biko's Café, as these are normally full of people around lunchtime who are (suprisingly) willing to sign up to most causes you can think of!
Now hand it back in to General Office making sure to leave your contact details. In a few days time, you should be given notice of a 'priorities ballot' - this is the chance for ANY ordinary student member to vote on what order they want the motions to be discussed at the GM. Get all your mates to vote/campaign for people to put your issue number 1 and you're sorted.
People are allowed to amend the standing motions up to approximately one week after they are published on the Union noticeboards and on the website. You can do the same to other people's motions, and you can either accept that amendment as a friendly one and let it be inserted into your motion, or argue against it at the GM.
Follow these steps and you should be sorted for getting your motion to a GM. Now you need to get out there, campaign, and make sure the GM makes quorum. This is when 300 people are in the room, the necessary number for the GM to go ahead. Let's hope your issue resonates with Manchester students...or you have a hell of a lot of mates!