I'm getting a lot of garbage, but I can't see a way of disposing of it! I'd assume that constructing garbage disposal buildings around industrial areas is the way to go, but when I click garbage disposal buildings, the list is utterly empty and this leaves me sad.

Oh I see, all I had to do was to designate a landfill and all seems to be better now, city has suddenly jumped back to life!

I think you have to put them next to land fills

Yep, initially landfill so that the garbage trucks dump the rubbish there. Later on I think you can get incinerators, but they cause pollution and people don't like to live near them. I think you can also make deals with neighbouring cities for them to take your rubbish for a fee.

Hire industrial junk removal experts to throw out the junk without any problem.