The process is the same as with other operating systems. You go to the laptop manufacturer's website and download the drivers provided there. If there's none for linux, it means it's not supported and you can't. At least officially.
Unofficially you can try googling around for solutions, finding drivers in repositories and stuff like that. The linux community may be able to help you, AMD almost certainly not.
With the HD 4200 you're probably stuck with open souce drivers as linux support for legacy cards is almost unexistant, even on the desktop side.
CPU: AMD Phenom II X4 810 @ 3250MHz | RAM: Kingmax 2x2GB DDR2 800 @ 833MHz| MoBo: MSI K9A2 CF v1.0 (BIOS: 1.D)| GPU: Asus HD 6850 1024MB (DirectCu) @ 850/1100MHz | Display: Chili Green Vision L24FHD | PSU: PC Power & Cooling Silencer 750 Quad | OS: MS Windows 95 x64 Edition
CPU: Pentium 4 Northwood S478 @ 3200MHz | RAM: 1,5GB DDR 400| MoBo: Gigabyte GA-8S661FXMP-RZ | GPU: Abit Geforce Ti 4200 | Display: Dimarson 19" CRT | PSU: Noname 400W | OS: MS Windows XP Pro, Fedora 18