The bottom line is that virtually all (except UNOPS and UNICEF) UN agencies do not pay interns, do not provide a stipend, housing or any financial support, but expect you to shoulder all your expenses. Yet, they will expect to count with all your time and energy during the time you are here.
You need to be aware that living expenses in Geneva are very high. Unless you come from a wealthy background and/or you will have support from your family or have sufficient savings, you will be facing a real challenge. What you need to do is to have a very realistic budget, and reduce your expenses as much as you realistically can. Living in France can help, as housing and living costs are lower.
You may be able to find ways of having some income - although you are not supposed to have parallel employment -, but you should not come with the expectation that you will. In addition, if you want to benefit from the opportunity, you will have to devote sufficient time to your internship, and that will leave very little time for any side employment. What may be realistic is to find an arrangement with a family (preferably UN staff) who is willing to provide you with housing in exchange for helping with their children.
Are you aware of David Hyde's case? It brought attention to how bad it can get for UN interns. This article in the Nation discusses the issue quite adequately.
Here is a very negative opinion on internships and their presumed benefits from a UN staff member. I disagree with that article, but as you will see in the comments, many UN staff and former interns agree with it.
You do walk away with the experience and contacts, but you should be aware that you can not seek employment in the UN for 6 months after the end of your internship, and that, depending of where you want to seek employment afterwards, many employers are not as impressed as you and I are with the UN.
To get the most out of the internship, you should be clear and realistic about what it is that you want to get out of it. While there are many generous supervisors who will look after you, there are also many who will just use you. The clearer you are about you objectives, the more you can get out of your internship.
As a citizen of a EU country and a UN Intern, there is no legal aspects that you should worry about. Public transport is quite good, though a bit expensive.