Answer:
First: Check the phone line to see if it's connected. This is always a first for most computer problems, esspecially regarding network connections. If a cable is loose, or not secured because of a broken tab, replace the cable.
Second: Check the properties of your dial-up connection. There may be an option or checkbox that is (un)checked when it should be the other way.
Third: If you suspect there may be a problem with the modem itself, use Device Manager to scan the device for errors. If there are obvious signs that the device is having an error, try using a different PC on the same dial-up network, or use a different modem. If the new PC/modem works, then that means your modem just took a dump.
Fourth: If you've checked all the steps above, and all else has failed, then there is a connectivity issue with the rest of the network. There can be multiple reasons for this. The most likely is that the network is down, or your ISP (Internet Service Provider) is currently not in service, probably due to maintenance issues or one of their servers is shut down. In this case, you'll just have to wait.
It is also possible that if you received your dial-up username, domain, and password directly from your ISP, they might have given you the wrong one, or there is a typo.
Call your ISP. Either they will tell you that there is a problem with their servers, they are undergoing maintenance, or your username/domain/password are wrong. In the latter case, ask them to give you a new one, they'll happily oblige and you can move on with your life.
(I wrote this in spite of the idiot that wrote "Get High" as the previous answer to this question. Hope this helped)