NOTE: Some versions of VLC require a small amount of tweaking to get this to work. Thanks to Michael in comments for making others aware of this. You will want to go to Tools >> Preferences >> Show All Settings >> Video >> Output Modules >> OpenGL. In Windows, Windows GDI Video Output may also work for you. Otherwise, simply follow the instructions as they are written.
If you are using the increasingly popular VLC Media Player to play your DVDs and/or media files, you probably also want it to upscale the video so that it displays more clearly. While a basic upscaling is always enabled by default (otherwise, the video would never be able to go full-screen or, in fact, at any higher resolution than the video was encoded at.) It is possible to increase the quality that VLC upscales, however. To do this you will have to go into VLC's settings and enable it. VLC has a lot of options and sometimes the sheer volume can see daunting and confusing, but this guide will explain it to you in a few easy steps.
First, go under Tools to Preferences.
Click "All" under "Show settings." The screen will then change to look like the following image. Click the "Video" heading under this. (It will appear like the following image, but for the sake of having less arrows per image, I highlighted the Video heading in the prior image.)
Click the "Video" heading on the left. A "Filters" subheading will appear. Click that, and the window will look as it does in the picture above. On the right hand side, click the "Video post processing filter" box and the "Video scaling filter" box. In the long white box at the bottom of that window, add the phrase ":sharpen" (the colon is necessary, make sure you do not add a space) to the already listed information.
Make sure before you proceed that you do NOT click these boxes underneath the "Video output filter" heading in the filters window. This heading looks nearly identical but does not do the same thing.
You're still not done, but you're very close. Scroll down the list under the "Filters" heading and click the "Sharpen video filter" subheading. This filte sharpens the image of the picture so that it is clearer. A good starting value for this is .15. The value on this setting depends highly on your source material.
If you're working with a DVD or a file that has been encoded in a high quality, you might want to set it as high as .25. If you're working with something of low quality, you might not want it on at all! The more the material is compressed (smaller file size and poorer compression methods, which in turn leads to more macroblocking) the lower you will want to set the sharpening value as it will sharpen the blocks and make them more noticable.
Follow down the list on the right hand side and click the "postproc" filter heading. VLC's video post processing filter removes the macroblocks mentioned above. In general terms, however, post processing can refer to any number of filters that can be used to enhance the displayed image of a video.
The level of post processing you set on depends mainly on your computer's processor speed and amount of RAM; the higher the number your computer can handle without making the video choppy, the better. 6 is the highest number. Start there, if the video isn't choppy, leave it there, otherwise, go incrementally down until the video playback is smooth.
One more step to go, the most important part of the upsampling process. The Video scaling filter is the most important part of the upsampling process. Click the "swscale" heading on the left hand side of the window. Clicking the drop-down box next to "Scaling mode" will give you a variety of options. There are a variety of scaling modes. I prefer "Lanczos," but "SincR," "Bicubic," and "Experimental" are all good options. Some videos perform better using different scaling modes (high action, low action, animation, etc;) and some scaling modes are less CPU/memory intensive than others. Lanczos, in my opinion, seems to have the best quality all around of all of them, but it can use more system resources, but your mileage may vary.
That's it, you're done. Click the Save box, and you're all set to go. If you had a video playing or paused while you did this, you will have to completely stop the video and restart it to notice a difference.
UPDATE (as of 1 August 2013): Since I've seen my guide linked and mentioned and reposted in a few places and found it accidentally using Google as well when doing searches, I've decided to update it with a bit of new information. By the way, using my blog posts elsewhere is fine. I would appreciate attribution - a link back to this post is great.
VLC in its newer versions has a couple of other filters that are useful when upscaling video from source material that has been highly compressed and macroblocked. You can find these filters in the same place as the other filters I've mentioned. The two that I consider of note are:
1.) The High Quality 3D Denoiser Filter:
This is good if you are working with source material that has a lot of noise and macroblocking. The default settings will only remove a little bit of noise. You will have to put the numbers somewhere around 15-20 to really notice a difference with heavily macroblocked material. The luma numbers are more noticeable with the chroma. You will have to tweak this each time you use it, as using too much of this will make your video look "smeared" kind of like an old VHS tape.
2.) The Film Grain Filter
This one is good to use instead of the 3D Denoiser filter; film grain will dither away the appearance of small macroblocks and other artifacts from the encoding process. Film grain is naturally in video shot on film anyhow, so it will look natural, at least for some people. I leave this one on all of the time. I put it on maximum (10) when I use it.