Here’s a brief overview of the steps between attaching the camera to my computer and the final image:

1. Store the images (see my image management overview);
2. Convert them from RAW (read why), store them preferably in a 48bit format - the better quality you start with, the better print you'll end up with;
3. Open with your favorite photo processing tool and crop first. No need to run all these expensive algorithms on parts of the images you're not going to need and if the cropping doesn't turn out anything interesting, you might just as well stop with the image and do something else.
4. Next play around with colors - levels, curves, B&W conversion, whatever. If you use Photoshop, use Adjustment Layers, this will allow you to play around a lot while always preserving the original image (and its quality). PictureWindow will keep every step around, you can save 'interesting' intermediate results as normal files (I also always save masks with PictureWindow);
5. Sharpen only as a last step (another reason to use RAW - JPEG images are already sharpened, and that's undoable). If you use Unsharp Masking, convert the image to Lab color and only sharpen the Lightness channel; if you work on GIMP 1.x convert to HSV and only sharpen the Value channel. Sharpening these layers will give you all the sharpness you need and introduces a lot less noise than when you sharpen all channels. There are more complicated sharpening procedures on the Net that work even better and even Photoshop plugins that do that all for you;
6. Save in the native format of your photo editing program (or TIFF - TIFF is a rich format with lossless compression and support for EXIF/IPTC annotations, color management, etcetera), and only as a final step export to JPEG. It is handy here to attach a title to the image number that comes from the camera - the title helps you in finding your photo, while keeping the number in the filename links the image to the original raw "negative".