Since not everything is HD, even stations that normally broadcast HD sometimes need to use SD video. In this case, they "upconvert" the SD video to HD.
This doesn't mean that video is now HD (you can't add resolution that doesn't exist). It just means the video has essentially been expaned to fit the vertical resolution of the station's HD signal. However, most SD video will have black bars on either side since it isn't the same size as widescreen HD video.
Sometimes SD video can look better on the HD channel than it normally would on the SD station. This is because HD channels get more bandwith (available space) on a cable or satellite provider. The SD video ends up with much less compression since the staion is being given enough room for HD video, which takes up more than 5 times the space.
Some stations place "pillar bars" on the sides of SD video to fill in the empty portions on the sides. Other stations stretch the SD video to fill the screen. The downside of stretching is it makes people look short and fat and and can make the video look more fuzzy by expanding it so much. A few stations use a "dynamic stretch" that stretch the edges of the video more than the middle. For the most part, this helps keep objects in the middle of the screen looking normal, but things at the edges will look warped. The last technique involves expanding the whole image to make it fill the screen. This has two problems. The first is that parts of the top and bottom of the video get cut off. The second part is the video can get very fuzzy when expanded that much.
Okay, so you're thinking, "I'll just look for pillar boxes or blown-up/stretched video and I'll know it's SD, right?"
Unfortunately, to make things a bit confusing, there exists a sneaky thing known as widescreen SD (also know as Enhanced Definition Television, or EDTV). It's lower resolution SD video, but in the same widescreen dimensions as HD video uses. The biggest use of widescreen SD is in sporting events where you can't use an HD camera. Racing uses SD cameras inside cars and golf often uses them for ground cameras that move from hole to hole. The reason for this is these cameras are often wireless. Most portable wireless technology doesn't have enough bandwidth to fit all that information HD video contains. As a result, those cameras would likely look worse if they were transmitting HD since the video would need to be compressed so much. Most reality TV shows use SD cameras since the shows often need so many cameras, or need very small "spy-cams".
When it comes to picking out SD video (even when it's widescreen), you can usually tell the difference if you pay attention. Even widescreen SD video will look a bit more fuzzy than the HD. Of course, if the whole broadcast is undergoing a lot of compression, the HD won't look much better. However, SD video becomes very obvious in a clean, high-bandwidth broadcast.