Your profile says you have a Canon 550D (and an AE-1 but I'll ignore that for the moment.) The 550D can only "meter" flash if it's shooting in E-TTL mode. In that mode the flash technically fires twice and the camera meters twice.
Here's a simplified version of how it works:
1) The camera fires a pre-flash at a substantially reduced power level (I think the default is 1/16th power but you can usually change it.)
2) The camera "meters" the scene in "evaluative" metering mode with no flash at all.
3) The camera compares the metering zones between #1 and #2. If it finds a zone with a bright point in #1 but is dark in #2 that this indicates a reflection (a shiny surface). If it finds a zone with very little change between #1 and #2 this indicates a light source within a room (e.g. a table lamp). It basically tries to ignore those zones (because they don't accurately indicate how the flash is illuminating the scene) and then compares the differences for the remaining evaluative metering zones (between #1 and #2) to detect how much of a difference the flash made (at 1/16th power).
4) Depending on the lens, it may be able to get focused subject distance information. Based on the guide number of the flash, the aperture of the lens, and the ISO of the camera, it can calculate the amount of flash power which *should* be needed to illuminate the subject. But even without that info, it can use the differences between the metering sample from #1 and #2 to determine how much of a difference was made at just 1/16th power, and then adjust to determine how much REAL power should be used to take the shot.
5) The camera then sets an appropriately power level to the flash and takes the shot (firing the flash again, but this time and the prescribed power level.)
ALL of this happens so fast, that if you didn't know it was happening, you'd swear your flash only fired once.
Canon calls this "E-TTL" or "E-TTL II". Nikon calls it i-TTL. Just about every camera maker has this or some variation on it.
That's the ONLY way the built-in metering on your camera can meter "flash"... and it only works for dedicated Canon E-TTL compatible flash units (or Nikon i-TTL compatible units for Nikon owners, etc.) If you take the flash out of that TTL mode and use it manually then your camera cannot "meter" the flash at all.
Going back to your AE-1... that technology was quite a bit different. Notice on the AE-1 there are only 3 contacts on the hot-shote (rather than 5). Technically the metal foot plate is actually the "ground" pin... so really your AE-1 has 4 electrical contacts (3 plus ground) and your 550D has 6 contacts (5 plus ground). The AE-1 doesn't have any form of TTL flash. It used a Thyristor-based flash system. In that system you'd set the Canon speedlight to either the high or low power mode. The speedlight would notify the camera that it was "on" and the camera would automatically set an aperture based on whether the flash was in the low or high power mode). The thyristor has a sensor on the flash gun which senses the return from the flash and then cuts off the power to the flash when it detects that enough light has returned. While this seems straight-forward and sensible... the PROBLEM with that system is that was easily fooled by highly reflective surfaces and or scenes in which there was a light-emitting source in the scene (such as a lamp). The current modern TTL technologies (such as E-TTL and i-TTL) are very difficult to fool because the advanced multi-zone metering systems in the camera and pre-flash are used to "test" the scene for reflections or light sources within the scene (and ignore them) so the exposure will be set based on what the "rest" of the metering zones showed.
So that's all great for TTL systems... what about for manual flash.
There are hand-held light meters which can tell you what exposure you need to set when shooting with flash on manual control. These meters measure "incident" light. You place the meter where you expect your subject to be and the meter "collects" the amount of light landing at the subject's location. This is basically the most accurate way to meter a shot (the built-in meter on your camera can only measure "reflected" light which bounces off your subject... that's less accurate because some subjects are either more or less reflective than others.)
Not all hand-held incident light meters can meter "flash". My first meter was a Sekonic L-308s... that's probably one of the most basic incident meters (costs a little over $200) which is also capable of metering for "flash" photography (you put it in a mode where it's expecting a flash and it continuously monitors the light looking for a huge spike in the light value... it locks onto that "spike" in light levels and then tells you what the meter reading would be. It's simple and fairly straight-forward. The Sekonic L-358 is more advanced and one of it's features is the ability to show you "flash contribution"... the percentage of light that came from flash vs. the percentage which came from ambient. This is VERY handy when shooting in mixed lighting situations.
If you're doing flash photography, it's nice to own a light meter which can meter flash. A light meter is one of those tools which I think just about every serious photographer (whether pro or enthusiast) should probably own -- even though you wont use it very often.