Broadband is what your local cable company usually offers. It is what is called a "shared" bandwidth. In other words, the more people that are online, the slower your connection can be. Broadband has it's advantages though, it's usually faster than DSL (Digital Subscriber Line) offering speeds up to 8Mbps and beyond- fast download speeds, and decent upload speeds.
DSL is what is run over your ordinary phone line. Each person has a dedicated line, which is your phone line. Unlike broadband, it's not shared bandwidth, so it doesn't matter how many people are online. The downside is, the farther away from the central office you are, your speeds can slow waaaaaaay down. DSL has speeds up to 8Mbps and beyone also, but in less places that cable has.
Dial-up is just that, dial-up. Consider the average modem communicates at around 40bps (1024b= 1Mb) and the fastest it can go, in theory, is 56kbps (ps stands for per second). I have DSL, with an average download speed of 1.5Mbps, wich is around 1536bps, which is 38.4x faster than the average dial-up speed. Hope this helps.