This may sound strange, but hear me out. My uncle gave me this advice when I moved out of my parents' house, and it did work. Establish the space as your own. Like others have suggested above, try hanging up photos of friends and family, or see if your folks have any furniture in storage that they'd let you use. Familiar things might help.
But then...take advantage of the space, and personalize it. A few suggestions: if you can get permission, repaint the place in colors you like. Take photos of your friends, or the area where you live, and hang them around; a friend of mine mats photos (cheaper than framing) and hangs them on his living room wall in collages. Whatever hobbies you have, make a place in the flat for them: a work station, a seat near a window for reading or studying, hanging hooks on the walls for art or instruments, shelves for books or items, a place for your sports equipment, whatever you like! Start inviting people over for game night, or study group, or drinks and popcorn, or anything.
The more memories you start to make in your new place, the more it will seem like yours. Even if (like me) you're pretty much broke, and can only make improvements slowly, the project itself is what will give you the feeling of the place being yours. For me, that sense of belonging helped the homesickness more than anything.
It might also help to learn the neighborhood where you've moved to. I've never been socially graceful enough to actually pluck up my guts and
invite my neighbors over, but if you are, you might find that helpful. But even if all you do is take a stroll around the neighborhood every day, you'll figure out the normal flow of the people who live around you, and that familiarity will help, too. (Worked for me, anyway.)
I've gone on and on here, and I'm sorry for that, but I hope this helps some. :)
