EDIT:
If you just want to see basic voltage, measure quickly as above at the atty connector. If the battery is freshly charged, it gives you a "starting condition" of a battery. For a direct PT, it will tell you the volts. I think the meter is fairly high impedance (megaohms) while measuring voltage. May depend on the meter. For amperage, though, the protected battery can decide that is is shorted and self-destruct, cut off, whatever. I haven't had one do that, but I don't go around shorting them either.
If you want to watch it (volts or amps) as you vape (much more interesting over time):
END EDIT
Gizmo. With a MM. Basic idea while vaping under load (which is your question I think)....
Voltage can be measured between any two points without changing the circuit. However, amperage is measured in-circuit (you have to break the circuit and insert the meter). The meter must be able to handle the amps.
This is hard to explain without a picture. The electricity flows through the meter as one of the connections, either the positive center, or the outer negative ground. The gizmo is used to "break" one connection or the other and allow you to "insert" the meter in circuit. This allows you to measure amps. Your meter probably had instructions on this. See online as well. Lots of stuff available on electronics and DMM use.
Insert a gizmo between your regular atty setup and the battery connector on your device. The gizmo simply has a gap that the DMM is used to fill. This gives you a dynamic readout of amperage.... The DMM has a minor resistance, but it should be insignificant with the amount of current we use for vaping. Note that amount of current can "blow" a meter (fuse) unless you use the proper amp setting... see your user's manual.
Let's say the center connector doesn't connect but the outside still does. This can be accomplished with two insulated wires ( insulated so they don't bridge the outer ground connection) sticking up through the shell of the gizmo and allowing you to attach a meter. Or you could have the center connected and not have the outer shell connected (plastic threads??) and bridge the outside with the meter. The DMM connects the gap and the amps are measured with the DMM. The atty would only work when the DMM is connected. The meter does NOT CONNECT the center positive to the outer shell-ground. It bridges the gap in EITHER one or the other.
I think someone (or more) has such a connector they use to take readings dynamically during testing. I'm not sure what they used to build it. EDIT: see/search this forum. HexKrak indicates that bigblue30 has some info.... he answered while I was typing this.
The gizmo is needed because it was my understanding that you wanted to watch the meter as you vape. It will give you connection points. You may not need a gizmo for voltage only, just 2 points to measure. But that's only 1/2 the story. The amperage and voltage will change over time.
Be careful with this... check for shorts. Shorting a battery without a resistor for any length of time (crossing the streams) is a bad thing.
Remember this??? <Ghostbusters>
Dr. Egon Spengler: There's something very important I forgot to tell you.
Dr. Peter Venkman: What?
Dr. Egon Spengler: Don't cross the streams.
Dr. Peter Venkman: Why?
Dr. Egon Spengler: It would be bad.
Dr. Peter Venkman: I'm fuzzy on the whole good/bad thing. What do you mean, "bad"?
Dr. Egon Spengler: Try to imagine all life as you know it stopping instantaneously and every molecule in your body exploding at the speed of light.
Dr Ray Stantz: Total protonic reversal.
Dr. Peter Venkman: Right. That's bad. Okay. All right. Important safety tip. Thanks, Egon.
Edit again:
P.S.
The interesting thing is that "what voltage you are vaping at" is different over time as the battery is depleted. Amperage changes too. Also, different batteries or power sources may provide different amperes even at the same voltage. Without knowing why you are asking the question, it's hard to explain, as it changes over time with a battery. May not change much with a direct connection.
I'm tired..... Good luck.