This subject is the most hotly debated issue, as it is so complex, difficult to achieve and vital to get right for good quality prints.
The following advice is based on my own practical experience using Photoshop. Many others would contest this approach, but if all else fails give it a try and let me know how successful you have been in getting faithful colours compared to the screen image.
When using Photoshop (full version, not LE) the Adobe Gamma calibration routine in the Control Panel should be run and the instructions carefully followed.
Most other photo editing packages offer some method for adjusting the gamma correction. Whatever method is used always use the same test image and never save this image, as you may want to use it again, unmodified. If in doubt re-install the package from scratch.
After trying out many experimental ICC profiles in Photoshop (and then reloading Photoshop from scratch after fitting a SCSI hard drive), I have come to the conclusion that the only colour correction needed for most home based PC systems is the Adobe Gamma Correction. Take time to do this and read the instructions carefully as a wrongly set up system will never print out a good picture. Selecting the correct background lighting setting is very important.
After performing a test print (with sRGB selected) compare this to the screen image. Hopefully this should be pretty close to the screen image. if for some reason it should be necessary to adjust the on-screen colour to get a better match, adjust the monitor gun balance by using the video card software, or as a last resort by adjustment of the monitor (not always available), and then carry out the gamma correction again.
Remember that to remove a red cast on the printed picture the screen image wants to also have the same red cast. You would then adjust the image in Photoshop to remove the cast, which should also remove it from the print. Gamma correction does not alter the strongest or weakest colours only the mid point by bending the colour input/output curve.
Should you have an overall unwanted colour cast, alteration of the gamma correction may only cure some elements in the picture and should only be used to ensure that a mid-point grey has no colour cast. Do not be tempted to play around with other ICC profiles, you can finish up like I dog chasing it's own tail, you have been warned!
Keep to the same inks and paper for subsequent prints, or use adjustments in the Epson printer dialog box if you use alternatives.
This page will be updated shortly to cover Photoshop 6.0