When reducing size of an image which contains text (e.g. Screenshots), the text in the image will become blur due to the anti-aliasing used in the resampling algorithm (Lanczos, ...).
Using a resampling algorithm (e.g. Nearest Neighbor) which does not do anti-aliasing would help, but the results are bad since the algorithm will simply remove lines and rows of pixels in the image and the image will not look that nice.
A good way to get both a nice image and readable text:
1.) Reduce the image's size with a good resampling algorithm, e.g. Lanczos
2.) Sharpen the image a bit ("Filter > Misc > Sharpen, e.g. 10).
If you don't like the result, you just undo (Edit > Undo) or reload your original and repeat.
When saving in lossy JPG format, you might get artefacts which will make the text less readable, again. So you should try to save the image in a lossless format. For images for the web I recommend PNG or GIF.
Sample screenshot (notice the tiny, but sharp text in the image):

Notes:
- Forum member "Lasse" has tested the resizing of screenshots containing text using various resampling algorithms of XnView. He provides the results on his webpage. His conclusion is that with only downsizing the results have poor quality.
- Post 'How to prepare an image for the internet?' might also provide interesting informations.
- This info is based on the topic Reduce an image with text makes text blur