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I used paper mache to make my horns. They're sturdy and lightweight, so... yeah. Awesome.

What I did was make a tinfoil core by molding the horn shape. I then covered it with tape, and then I used ordinairy glue combined with a little bit of water, and then I used toilet paper to create a pasty, smooth surface.

After it dried, I sanded it and then I used printer paper for the final layer.

This works best with small horns, but if you're using a headband for your attachment method, the size of the horns don't matter.

Pic:

I used acrylic paint. I used wire to hold my horns in place.

What you do with the wire is that you drill a hole in the bottom of the horns (or puncture them with scissors... that's what I did, but you should form the hole in the tin foil and be careful not to plug it up). Then, you get some sturdy wire, the stuff from a wire coat rack will do. It should be about a foot long for each horn, but that varies on the horn size. Obviously, you're going to want the wire to go deeper in larger horns so they don't wobble around so much.

Get a hot glue gun, fill the hole's opening with glue, and quickly stick the wire in there. And I mean QUICKLY, or else you'll wreck it and have to make a new hole, or re-drill it. Repeat with the other horn.

Then, stick them through your wig and bend the wire into a spiral shape. They should stay in place and you can easily unscrew them from the wig. It might take a few tries to get them placed right, though, and be careful not to rip your wig's netting. I think this is better than the headband method because you can usually see a headband when it's worn on the outside, and you don't have to ruin a wig to put the headband on under the wig and poke the horns through. (Although if you have money and wigs you don't intend on re-using for another cosplay, I think that's the sturdiest and nicest looking horn attachment method.)

Or, if you still want to use a headband, find a skinny plain black one covered in fabric. Plastic headbands are too shiny and it kind of ruins the "Look at me, I have hoarnz!" illusion.

Eh, I buy wigs on Halloween when they're more readily available at stores. And Goodwill. I found a really suitable wig at Goodwill that I can use for a Karkat, Jane, Jake, or John cosplay. And maybe Sollux? I don't know.

I haven't found any wigs at Goodwill at all.
Karkat, Jane, Jake, and John all have similar, tufty/messy hair! Just a little styling on the same short black wig and you should be good.
A link for a horn making master guide that should be easy to read through (I would suggest aluminum foil for the inner base, model magic/paper clay for the outer shell, Mod Podge for sealing, and I prefer wire (like you put the wire through the weft, and so on and so on): http://homestuckcosplayhelp.tumblr.com/post/32747099615/troll-horn-master-guide
Horns attachments that I liked (but never tried. Look through them and see what you like!): http://homestuckcosplayhelp.tumblr.com/post/14827908597/i-tried-using-the-horn-attachment-method-outlined
http://homestuckcosplayhelp.tumblr.com/post/8771188668/you-attach-the-horns-to-wire-while-they-are-being-made

YES!!! THank you! I will definitely check this out.

Well, you don't have to wait 3 weeks. I just happened to have that span of time available. I think for my first horns that didn't end up cracking, I only waited a week and it was completely fine? It might speed up the process, if you keep them in an dry, breezy area? When you feel them, and they don't feel too squishy or slightly moist, I'd guess they're ready. : )
(Either way, if you have clay to spare, I'd make two sets of the same horns, just so you have a back-up.)

Mod Podge is a glue/finish/sealer type liquid, easily found at most craft stores? I even saw them in the dismal art section at Walmart. Cheap too! I don't know if I was applying it on properly, but I always use it as a sealer after waiting for my color paint to dry -- adds like a protection coat to help prevent chipping of the paint, and I use the glossy one which makes my horns shiny. They also come in matte, if you want to avoid the shiny effect.
http://www.joann.com/plaid-modge-podge-8-oz-gloss-lustre/prd2193/

As for how long it took, do you mean like the entire process? I think it really shouldn't take more a solid week--most of that time is drying. To attach the horn onto my wig, it takes a few minutes to sew them in because I use those wigs for multiple other cosplays so need to detach and attach.
Another cool way I've seen someone attach it is:
http://m17un45f1n3455.tumblr.com/post/48755691446/i-figured-out-a-way-to-attach-horns-to-my-wig-no
I haven't tried it myself, but looks like it'll work!

Well you could always use a 3D printer?