Michael, a very basic, rough rule of thumb is that you can handhold a shutter speed that is the reciprocal of the focal length you're shooting at, so a 50mm lens can (using the rough guide) be hand held at 1/50th of a second (in real life, the normal step that falls at is 1/60th. However, on crop bodies (sych as yours, the crop factor has to be taken into account - so your 50mm has the same field/angle of view as an 80mm lens on full frame, so (in theory) needs a faster shutter speed to hand hold - 1/80th s (probably 1/90th in the real world.
Short lenses (wide angles) generally can be handheld at relatively long exposures - at 24mm (on a 1.6 x crop), 1/38.4 s, and at 70mm, 1/112th s. Once you get into telephotos though, the hand holdable times are shorter - at 100mm, you're looking at 1/160th s and at 300mm, 1/480th s. This is why standard zooms and kit lenses often don't have IS/OS/VR/VC but longerlenses do have it, allowing them to be used in lower light without a tripod. It's also sometimes the slower lenses (the ones with a higher f stop number) that need VR/OS etc - they need more light wide open and OS can make a big difference to their useability.
Don't worry too much if your telephoto doesn't have OS (although it's worth having and can be very effective) - a good tripod will hold the camera and lens steady for longer than OS will! (Beware of cheap tripods though - often a false economy!).