I use all three in my house so let me show you how I use them (I am on Virgin Cable but the principle is similar for ADSL).
1) Modem: When i first got broadband they gave me a modem. I was only able to use ONE computer on that broadband connection.
2) Router: I then bought a router and plugged it into the modem (on Virgin cable the modem and router are separate).
I was then able plug 4 PCs into the router that could all connect to the internet.
3) Hub: One of the ethernet wires that I plugged into my router I ran to my office upstairs. But because I only had one wire in my office I was only able to use one PC.
So I bought a hub and plugged the single wire into the hub in my office.
I can now use 4 PCs in my office (if I wished) all plugged into the hub, which itself is then plugged into the router.
Note a hub and a switch are very similar and you will often see these words used.
http://ask-leo.com/whats_the_difference_betwee n_a_hub_a_switch_and_a_router.html