Caring for your Supplies
Now that you've bought your paint and brushes, you'll want to make them last. Brushes in particular will last much longer if you care for them well. As a beginner, I had no idea how to look after my brushes and I wrecked a few of them out of inexperience. Here's what I recommend, based on my own trial and error:
Paint
Your paints don't need very much care. Just make sure you cap them tightly without cross-threading so they don't dry out. If you get serious about painting, I strongly recommend getting a tube wringer to avoid wasting paint, but it's not necessary at the beginning. If you're using professional quality paints, it will pay for itself pretty quickly. Also, it's great for toothpaste tubes!
Brushes
Cleaning: After painting, wash your brushes out well under the tap, making sure you get the paint out of the middle. Rub the bristles fairly hard with your fingers. Use a wee bit of mild soap if necessary. The brush hairs will get stained over time, but this won't affect their use. I'm embarrassed to say I bleached my brushes one time when I was a beginner, which caused all the hairs to dissolve. Don't do this - just wash your brushes well after every painting session and they'll be fine. It's worth it to get a small cake of brush cleaner to clean and reshape the bristles, but not essential if you're on a tight budget.
If your brush dries with acrylic paint on it, the brush will be ruined - you won't be able to get the paint out once it has dried. Leaving brushes in the jar of water will prevent them from drying out, but isn't much better for them. Never never never leave your brush in the water overnight. Sitting in the water too long can warp the bristles and waterlog the handle, causing the ferrule (the metal sleeve around the end) to loosen when it dries out. It's best to take a minute or two and wash your brushes out after every painting session, reshape the hairs with your fingers, and let the brush dry horizontally.
Storage: After cleaning, when you store your brushes, make sure they have ventilation to dry and the tips are protected. A typical pencil case (and even some brush holders I've seen for sale) won't work very well, because the brush tips can get bent against the end and dry crooked. I recommend just rolling your brushes in a rag, making sure to cover the ends, and secure an elastic band.
Replacement: It's up to you when you want to replace your brush. When brushes start to get old, the hairs don't form a good point, and the tip tends to split into clumps or get fuzzy, causing streaks in your brush strokes. If this is bothering you, it's probably a good idea to get a new brush. As a professional artist, I replace my brushes about every two months, but if you're a hobby painter you can use them much longer.
Canvas and Surfaces
It's obvious that you should try to keep your painting surface clean and protected, but it's harder than it sounds when you're traveling. For a sketchbook or watercolor pad, I recommend keeping it in a clear plastic reclosable document envelope from a stationary store. This way you can throw it in your bag without worrying about bending the pages or spilling on it.
Do have fun and be adventurous with your new supplies. You'll be replacing these ones eventually if you discover that you like painting, so don't be afraid to go ahead and use them up.