Lara -
The advice you've received so far is great. I agree with Ed that it starts with the ear. I'll bet that you can actually already hear more than you think you can, and that with a little practice things will open up for you.
I found that if I can see the notes in my mind and hear them in my ear at the same time it's easier. A free resource to help you both see and hear the intervals can be found at the
GNU Solfege site. Of course the site Hags referred you also looks like it could help you too.
Hags gave a good list of songs that highlight intervals. If you want a whole bunch more, so that you might find the ones you can most easily remember, take a look
here.
Keep after this - it will be worth the effort and you'll get it in short order!