Add more memory, more hard disk, a faster processor and other stuff depending on your needs, wishes and budget to go beyond the merely usable. In general, one big difference from DOS is that with Linux, adding memory makes a large difference, whereas with DOS, extra memory doesn't make that much difference. This of course has something to do with DOS's 640KB limit, which is completely nonexistent under Linux. All models of 386s 486s, Pentiums, Pentium Pros, Pentium IIs, and clones of these chips should work. Ports are also being done to the ARM, StrongARM, and MIPS architectures.
More details are available elsewhere.
Linux puts higher demands on hardware than DOS, Windows, and in fact most operating systems. This means that some marginal hardware that doesn't fail when running less demanding operating system may fail when running Linux. Recent 2.1.x kernels and later are able to detect more memory in a system. These lists are incomplete, and always will be. A full list of supported chipsets alone takes over a page.