The Recommended Minimum System Requirements, here, should allow even an inexperienced user to easily install a usable system with enough room to be comfortable. A good "rule of thumb" is that machines that could run XP, Vista, Windows 7 or x86 OS X will almost always be a lot faster with Ubuntu even if they are lower-spec than described below. Simply try Ubuntu CD as a LiveCD first to check the hardware works.
Ubuntu Desktop Edition
1 GHz x86 processor (Pentium 4 or better)
512 MiB of system memory (RAM)
5 GB of hard-drive space
Graphics card and monitor capable of 800x600
Either a CD/DVD drive or a USB port (or both)
Internet access is helpful
(For reference see https://help.ubuntu.com/11.04/installation-guide/i386/minimum-hardware-reqts.html.)
Hardware produced in the last few years or with an efficient architecture or machines built for a specific purpose can often work well with less. For example, a...