I've just bought a second hand road bike which doesn't have Quick Release Skewers.
Can I just buy a set of QR Skewers and fit them?
Are they a standard size?
Are there any gotchas waiting to bite me if I do change to them?
Is there anything specific I need to look for in order to change to QR Skewers?
I'm not sure if you intend to replace the axles themselves, but AFAIK, most nutted axles are not hollow, which means they can't accommodate QR skewers. If this is true in your case, you will need to replace the axles outright in order to use QR skewers.
QR axles for modern hubs do come in a few "standard" sizes, but you will nevertheless want to measure the dimensions of your frame and hubs anyway, in case they are not standard. You mentioned your bike is second-hand, which indicates it might be older, in which case this is doubly so.
There are three dimensions to check:
Hub spacing - This is the distance from the inside of one dropout to the other. You can measure this by removing the wheels from the frame and sticking a ruler in the dropouts. To replace the axles, you will need to find QR axles and skewers to match your hub spacing.
Otherwise, the QR may be too short or too long for the hub. With non-QR axles, an axle that is too long is not a problem (the nuts will still go on fine, and if you need to, you can cut the excess axle), but with a QR axle, you can't really trim the axle, because the QR skewer can't be trimmed.
Typically, hub spacing on modern bikes is 100 mm (front) and between 120 and 130 mm (rear). Again, you should measure this yourself-- I'm just giving you an idea of what these numbers should be.
Axle diameter - The QR axles you get should match the diameter of the existing axles so you can re-use the existing cups and locknuts (unless you were planning on replacing those, too).
Common axle diameters are between 8 to 10 mm, or 5/16", or 3/8".
Thread pitch - This is basically the angle of the threads on the axle. Like the diameter, this will need to match the existing axle if you want to re-use the cups. According to The Sheldon, thread pitch is measured in either threads per inch or millimeters per thread, with a 1 mm/thread pitch being equivalent to 25.4 TPI.
Common thread pitches include 1 mm/thread, 26 TPI, and (rarely) 24 TPI.
The axles need to be hollow QR axles; if they're solid you obviously can't put the skewer through it. You can replace the axles as well, but that starts raising the complexity level.
Otherwise, skewers are basically standard. You'll need to get them in the correct lengths for front and rear. For new, the Shimano ones are quite nice.
Replacing solid with hollow axles can be done, but as noted above the dimensions must be exactly right. As well, you will have to completely take down the hubs and re-establish the bearing adjustments. Normally, if you have the hubs apart, you'd be advised to replace the bearings, as it's standard mechanic's practice not to re-use them.
There is an alternative system called Axle Release available that puts a special nut on each side of the axle, which looks like a quick release lever. Both are done/undone to install the wheel.
You can see how it is installed in this video
