There are different ways to put up mohawks and liberty spikes. The original way to do it was to use raw eggs, but this can get a little smelly. You can do it that way, though. Here is what I like to use:

elmers glue and aqua net
a blow dryer
a comb


Those are my preferences, anyhow. They work the best and are super cheap, or can be stolen quite easily. Aqua net can also be replaced with Rave 4, or any strong hair spray. Get the elmers glue, preferably the clear non-run kind. If you're really opposed to elmers glue, you can use some really expensive hair glue, but I wouldn't recommend it, especially if you're on a budget.

Mohawks:

First it depends if you're going to be doing spikes or fans. Spikes are when you have spikes going across, and fans are when its just one long fan with no gaps in it, although sometimes gaps are inevitable.

Fans:

These are somewhat harder than spikes, but I think they look the best.

You will need to comb up a chunk of your hair, and spray it with your hair spray. Then, still holding your hair up, blow dry your hair until it is pretty stiff. Then you will apply the glue to the rest of the hair, and continue to blowdry until it is stiff. Do this in chunks of hair, and then take your comb and you're going to have to comb through all the hair so it looks like its all connected. Then it's good to add some more aqua net and glue and blowdry it more so it's really stiff.

Spikes (still mohawks):

Basically, it's the same thing as fans except you're going to do it in spikes. You hold up your chunk of hair that you want to be a spike, first spray hairspray on it (get the bases really well), blowdry, then apply glue. Repeat until you're satisfied.

Liberty spikes:

These can be pretty tedious. I used to have liberty spikes, but then I got a chelsea hawk because I decided they took too long. Liberty spikes can take up to two hours putting up, so you'll need to have a lot of patience. It's the same thing as mohawk spikes, except you're going to be doing it for your whole head. If you're a girl, I suggest leaving some bangs in the front so you don't look like a guy, and with mohawks too.

Take your chunk of hair you want to be a spike, spray it with hairspray, then blowdry stiff, then add glue. Repeat until done.

There are other things you can work to put up mohawks, and different ways to do things. Some kids use knox gelatin, I've met other kids actually put acrylic paint in their hair to color it. It just depends.