Firstly, I hate posting this. I was a newbie once and can remember the frustration of trying to understand what was going on.
OK, here goes.
I just had a look on eBay, there were 15 modems listed with no reserve and finishing in the next 10 minuets. 10 of them will just plug in and work under linux and 6 of those where under $1.
Because a lot of manufacturers think there way of making modems is the best (in most cases read "makes the most money"), there is a flood of modems that don't use the standard, well documented, simple to implement modem commands.
The majority of these are "winmodems", devices that are (in simple terms) nothing more than a way of plugging a phone line into the PC. All the work is done with the manufacturers own proprietary (ie. closed source and they wont tell you how it works no matter how nicely you ask) software. A lot of people have dedicated a lot of time (for free) to getting this crap (sorry, I cant call them modems) to work with linux.
There are also almost conventional (ie. hardware) modems that do not stick to the standard ATZ commands and a mix and match of all kinds rubbish in between.
So please, unless you are a sucker for punishment and would enjoy hours and hours of trying, testing, trying again, and again, and again..., Have a look here:
Or in the hardware compatibility list on this site, or any of the other reputable linux hardware sites. Then go to eBay or a locale flea market/garage sale etc. and spend no more that $5 for a used modem from a manufacturer that knows what standards are and how to stick to them.
Sorry for being an a**hole but I do not want to support manufacturers that cant stick to well established standards for the sake of their own (and microsoft's) profits.
I cant just leave it at that though.
Firstly, you need to know what your modem is. For serial port modems you will have to check what is written on the box. For internal modems, typing "lspci" in a terminal should give you enough info to get started. If it is a pci modem and it doesn't give any info here, taking it out and hitting it repeatedly with a hammer is the best solution as it is the worst kind of dirt ever put in a PC case.
When you have some info, search the hardware compatibility list above or the list here and see if it is possible to use it. If not then follow the same procedure as unidentified pci modems.
If it is possible but needs work, well, google is your friend, and so is the search function on this site and others like it.
If it is a definitely a hardware modem and it isn't responding, read up on ATZ commands and try changing settings, and test, and change, and test...
Post back if you are really stuck.
Sorry for the negative responce,