Very good advice, indeed. If you have the chance when you go out, take your mouthpiece with you and buzz whenever you can (just don't do it on a bus or something, it tends to annoy people). When watching TV, buzz. When reading, buzz. When studying (unless it bothers you to), buzz. You can never buzz enough.
Long tones and minor lip slurs (G -> low C -> G -> low C -> G, F# -> low B -> F# -> low B -> F#, etc) are a good way to start. Start using scales when your comfortable range (what you can play without straining or squeezing the horn to your lips, which you should never do) reaches the top of each scale. When you get more comfortable playing, find small tunes to play. A good way to work on fingerings and finger dexterity (which you will need for corps-level playing) is drilling the chromatic scale over and over. Go from the bottom of your range to the top chromatically, then back down, then back up, then back down, as many times as you feel you need.
Air is very important. Make sure you use breathing exercises (in 4, out 4; in 3, out 5; in 2, out 6; in 1, out 7), but don't strain yourself. Try doing such exercises with and without the horn to get a feel for the air resistance (make sure not to breath in through the horn; try keeping all three valves down for even more resistance). If you have the spare cash, get an AirMax Breather. It really does help, when used correctly (just read the instructions).
Main point: push yourself every time you pick up the horn, but don't strain yourself. If you push yourself too far, you could end up damaging something, which will only hinder you.
Good luck with learning mello.