I need to replace my Acer Desktop dial up modem. Can I do it myself and how?

This is a very simple process. Simply remove the cover of the CPU, remove any screws holding the modem in place and unplug from the mother board. Plug your new modem into the now open circuits, then proceed with installing any new drivers.

Ok - Here is a picture of a motherboard:

I suspect your existing dialup modem is in an existing PCI Slot on your motherboard, remove the existing dialup modem and "snap" your new one in it's place.

Use the software that came with it to get the correct drivers to work on it, (though I do believe XP and Vista will install without special drivers), but having the correct one for the modem you put in will insure it's working properly.