The Viewing:
I'd always recommend going to see a few cars before going with the intention to buy, this way you can familiarise yourself with them. To do this, I wouldn't waste a private sellers time but perhaps visit a dealer that has a car you wouldn't normally buy; not the spec you're after or mileage too high etc.
If this isn't possible, then at least look at as many adverts as possible to get a feel for things like differences in bumpers, facelift models, wheels and interior trim. If you see a car that should have a facelift front bumper or headlights for example, and doesn't, it may be a sign of repair.
When you arrive, scan around and check if it is indeed in the same location as the advert pictures and take a note of roads on the way there you could use on the test drive.
Before even knocking on the front door, have a quick look at the bodywork for any obvious signs of repair (I'll go into this in a LOT more detail) and feel the bonnet to see if it's warm. If the car has been warmed up before your arrival, that can be suspicious as why did it need to be?
My personal preference is to check the bodywork first and make my mind up on whether a test drive is required after that.
Quick Checks:
Look to see if the numberplates have dealer logos at the bottom. If it has original plates, that's a nice sign. If they don't match then it could mean anything from accident damage to a simple case of deterioration that required replacement for an MOT.
Similar marking can be found on the glass; again, if there are any discrepancies here, it could mean replacement or potentially a previous break in.
Check for missing smaller trim pieces, ideally you would have spotted these in the advert but if not, look for things like missing tow-eye covers, jacking point covers or washer jet covers for example. These could all be very innocent things but they are worth noting to look further.
See here for example where the washer jet trims and tow eye cover is missing; this suggest the bumper has been removed and re-fitted poorly. It also draws your attention to the larger than normal panel gap between it and the bonnet.
Checking VIN numbers is a good habit to get into, they can normally be found in the lower section of the windscreen, or on a plate in the engine bay, or even stamped into the body somewhere. You can check these against the others on the car and the V5C to make sure they all match. If there are any discrepancies, simply walk away.
More obvious defects that are noticeable in the flesh, if not in the advert pictures, are panel gaps and differences in colour between panels.
The silver car pictured below has had a front wing replaced and re-sprayed; you can see that the shade of silver is different to the surrounding panels and the gaps around the wing are not uniform (you'll also notice the crease by the rear light).
The white car has had similar work as you can see the alignment between panels is not correct.
Detail Checks:
More subtle signs of previous repairs will be in more hidden areas. I like to check rear quarter panels first as they're normally not removable like a bolted on wing or door. This means any repair will be more obvious. The arrows show where these panels normally meet others; in the case of a rear quarter panel, there is normally no obvious 'edge' where they meet the roof, so evidence in these areas are harder to hide.
Lesser bodyshops, or 'driveway repairs' may leave overspray in door-shuts and on un-masked trim. The examples below show overspray inside a front wheel arch (silver) in a door-shut area, near the latch (blue) and in the petrol cap recess (red). The last example is on a commercial van where the repair was particularly poor and obvious.
Panels that can be unbolted and replaced if damaged may be harder to spot, as they will have been painted off the car and there won't be any overspray to look for. However, newer paint stands out against older paint, and any screws / bolts will show signs of being removed (chipped paint).
Some manufacturers don't paint engine bays as thoroughly as exterior bodywork, so the engine bay will have a different finish, or colour, to the exterior panel. This can also highlight repairs as many bodyshops will paint to an edge, and not replicate the original 'blend'.
Rust; as it's 2018, chances are, whoever is reading this will be looking at cars where rust isn't a huge issue. I'll touch on it briefly here for completeness.
Don't underestimate a small bit of rust, as you can see in the images around a boot lock, what looks small under a piece of trim is actually quite significant.
The bonnet edge also shows the same; a small stone chip left untreated can spread needing a larger repair later on.
One item I advise looking for, no matter how new the car is, is any rust around the windscreen. Modern windscreens are structural and bonded to the car body, when replaced, they need cutting out. This creates heavy scratches on the inner, unseen, lip. If this isn't treated with the correct primer before a new screen is fitted, it will cause rust. This rust starts in an area you cannot see, and by the time it's visible, is indicative of a larger repair requiring the windscreen to be removed again.
Another tell-tale sign of previous repair are paint edges; these are where a part would have been masked off to protect them from new paint. However, if not done correctly, they leave a lip where the new paint built up against the edge of the tape (no difference to when you mask off doing DIY).
Below are various examples of this; the last two around a rear quarter panel as mentioned earlier.
In Green: When the boot was opened, you could see evidence above the rear light.
In Blue: Rear window trim that wasn't removed before painting, and instead masked off.
The general paint finish is also something to look for; 'orange peel' is a condition where the surface of the paint has the texture of an orange peel...
The example in blue is due to having the bonnet re-sprayed but the example in black is of a new car. Some modern cars can have a slight orange peel effect straight out of the show-room, due to modern paints. However they should never be as bad as the blue example.
Sometimes the paint can look smooth, shiny, well matched to other panels, but look closer. These are example of panels that have been re-sprayed with defects underneath the surface; the first two have had stone chips painted over, so you can see the 'crater' under the new paint. The last picture is a defect where the panel wasn't thoroughly cleaned before painting, causing 'fish-eyes'.
Another 'sub-surface' defect can be sanding marks, where a panel has been repaired, and during the process, sanding was required. This wasn't done properly and the effect can be seen in the final top coat. Although the surface might look smooth as the light catches it, the defect is in the lower coats of paint. The illustration (don't laugh) shows heavy sanding marks or scratches in the primer and how this shows through the top coat.
Runs in paint can sometimes be very obvious, but sometimes much more subtle. The first example shows how the metallic coat has runs that have then been lacquered over, so although the surface is very shiny and smooth, the finish underneath is poor. The second example is an extreme case and shows a very poor repair.
The last example shows what I was talking about with re-painting a panel that needs blending into the roof. The body-line has been use to try and hide the blend (normal practice) but can still be seen in the right light.