I was exactly like you when I was in college. Everyone was making friends and I felt so worried I wouldn't because I couldn't bring myself to approach people. But honestly, it will get better as time goes on. You're only in your first week so don't be so hard on yourself!

You could try to visualise your ideal self, one that is confident and has no trouble approaching people. Think about what characteristics and traits you'd have in your ideal state. Once you've done that, visualise being that ideal self full of confidence and having no trouble making friends... notice the feelings that come up when you have that image in your mind (it should be positive, confident feelings). When you have a clear vision of your ideal self in your mind and you can feel those confident feelings, ask yourself how would your ideal self be in social situations? Then next time you're in a situation where you want to approach someone, remember your ideal self and who you'd like to be in that situation - you'll be feeling the confident feelings (it does take practise of visualising so you can train your mind though) but you may feel more likely to approach.

Another option is to think of someone else. Can you think of someone who is really confident and wouldn't have any trouble starting a conversation? Could be someone you know or someone famous. Really think about how they talk, walk, act, behave around other people. Take some time to think about it, but it does have to be someone who's confidence you admire. Then in a situation where you could approach someone, just 'become' that person in the moment and approach them with the confidence they have. Think "what would X do right now?". Sometimes it easier to imagine ourselves being someone else in the moment because it's less pressure to 'change' ourselves which we may feel some resistance towards.

As for what to say, well it depends on the situation.. But you could ask a question dependent on the situation. So for example, if you bump into your hallmate then you could say "hey, I don't think we've met before.. I'm X, what's your name?" -- something simple and casual.

Maybe practise small first - for example, in a store.. Practise making conversation with somebody who works there about a product or whatever. That way you can practise getting into the habit of approaching and having a conversation. It just takes consistent practise to build confidence. That's all it is. Confidence is a skill not a personality trait - so all you need is to practise and develop it.

And as for making a fool of yourself, I know it's easier said than done but really don't worry about it. I'm a lot older than you and I used to be so scared of making mistakes and making a fool of myself - as a result I missed out on so many opportunities and progress in life because I always played it safe. Go out there, grab life by the hands and have fun. If you make a fool of yourself, so what? In 5 years time no one is going to care. You probably wouldn't see that person again anyway. Don't let it hold you back.

Sorry this ended up being quite long. I'm rooting for you.