First, you asked what the labels on the connectors of the power supply mean:
From right to left:
Earth - connect your earthing wire to that. The wire should be green and connect to the earth pin of your mains cable, and if you're using a metal case for everything, also be attached to the case so that the case is grounded.
N AC - mains neutral, should be connected to the gray or white wire of your mains cable
L AC - mains live, should be connected to the black or red wire of your mains cable.
-V - -15V output. If you have no other electronics besides what you mentioned, you can leave it unconnected.
-S - sense wire for the -15V. This must be connected to -V somewhere, the easiest way is right at the power supply (it has a small metal plate for this purpose.) For more precise power regulation, run a separate wire and connect it to -V as close to your load as possible.
COM - Ground, connect this to black wire of your load cell.
+S - Same as -S explained above, but for +V. It's ok to just use the metal plate and run a separate wire.
+V - +15V output. Connect this to the red wire of your load cell.
You mentioned that you considered buying a wallwart and stripping it to power your power supply. This implies to me that you haven't realized that this power supply is supposed to be powered directly by mains. Connect it to the AC wall socket by a simple 3-wire cable (which connects to earth, N AC and L AC as outlined above.) If you don't have one, you can make do with buying an extension cord and cutting the socket end off, then stripping the insulation off the wires so you can insert them into your power supply sockets. Do think about what you're doing in this instance, as you have exposed metal contacts here with mains voltage on them. Absolutely do unplug it at the wall if you do any work at all on the system.
And typically, a power supply like this would not be exposed but live inside some sort of box with the rest of your electronics, and you'd use an AC entry socket, something like this:
http://www.newark.com/bulgin/bzv01-z0000-01/connector-power-entry-inlet-plug/dp/06WX9357 . I do recommend you use something like this, since it has a nice switch, a fuse, and prevents you from touching any live parts.
Next, the load cell. There is a diagram explaining the wire colors and functions in this datasheet here, page 3 at the bottom:
http://meas-spec.com/downloads/ELHS.pdf . The load cell is a fairly simple device electrically, and you will not damage it even if you hook it up wrong, as long as you only have 15V in play. The one you picked has no overload (as in physical force, not electric power) protection though and very little margin (1.5x overrange, so 7500N is the limit over which damage may occur), so be careful in the construction of your apparatus. If you do overload it, the damage might not be immediately obvious, but it will no longer be accurate.
In the load cell datasheet linked above, it also tells you what your DAQ needs to be able to handle: on page 2 there's a table that says the FSO (Full Scale Output) for your load cell is 200mV with a 15V supply. So if you apply 5000N, you get 200mV between the green and white wires., and they'll still be roughly at 7.5V above COM. It's also roughly 0.5% accurate, so if that's the accuracy you're going for, you need to be able to resolve 1mV. If your DAQs differential inputs that don't mind the 7.5V, 16bits resolution at its +-1V scale are easily enough, in fact you need just 11 bits. If you can't use the differential input, and use two single ended inputs with the +-10V range instead, you'd then need 15 bits of resolution, out of the 16 you have available. Your DAQ is pretty nice, so it should be able to just about handle that.
Btw, if you have temperature changes for some reason, more than about 5°C compared to the temperature you calibrated the system at, you need to think about measuring it and compensating for it. But that can always be added later.
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