I'm still confused on it too...but Microsoft Paint so far has been the only image program I've needed. You can open the image there and then go to File, Save As... and from there there should be a bar on the bottom that has the image depth or file type you want to save to. Drop it down and you should find a "256-color (8-bit) bitmap (.bmp)" or something similar. Save it as that and the colors will automatically adjust. If you don't like the colors that adjusted, even though Paint typically has a bad original 8-bit palette preset on the bottom, you can double-click on the boxes of colors to change them. The color you select, though, when put into the image, will 8-bit itself, so what you select or adjust may not be an 8-bit color. You can change colors around until you find good replacement colors for the ones that warped after the file-save. I know that sometimes in Paint, yellows will turn to a bluish gray when I save a PNG or 24-bit image to 8-bit. Makes it hard when you take a pic of someone's face you wanna put in your game and then their face turns weird colors, but like I said you can change colors in Paint and Fill-Bucket those areas. (in case you don't know, Fill-Bucket is the icon with the spilling paint bucket. Fills in an area of the color you click it on in the image. If you already knew, good.)
A complex method I use to find good colors: I open two instances of Paint and have one open the image I need to edit, while the other opens a standard sheet from RPGM's folders, usually a CharSet image. Using the Highlighter tools and the Copy&Paste (Ctrl C + Ctrl V) I copy an area that has the colors I need, go to the image that needs editing, and paste it nearby. Then I can use the Color Pickup (the eyedropper tool) to pick the colors I need. Because the RPGM sets are all already 8-bit colors, they have the colors I need so I don't have to go through and trial-and-error color changes. Came in very handy when I made Cloud and Sephiroth sprites for my game. Instead of trying to get the right yellows and stuff I found them on clothes and hair of various hero charsets.
Yeah, 8-bit limitation on images is annoying at times...but with enough screwing around with Paint or some other image program you'll get the gist of it.