Taking a manual blood pressure v. an automated one (even though a manual blood pressure is still an non invasive blood pressure (NIBP), people usually write NIBP instead of automated) have their own pros and cons. Some people may say that you should take a manual blood pressure before using a NIBP to watch for trending, or they'll take a manual blood pressure to confirm what they got by NIBP, but in my opinion, it doesn't really matter. You should consider everything. If you get something way different from manual, or something way different from NIBP, you should consider that you're doing one of them wrong, not automatically assume that the manual blood pressure is right, which seems to be what most people assume.
I assume you already know the motion to do it even though you said you'd like to learn how to do it.
Things that help in my opinion is palpating the brachial pulse above the antecubital fossa (above the bend of the elbow), and place the diaphragm/bell of the stethoscope there.
I believe the AHA still recommends using the bell, the part people confused to be "the pedriatric side", of the stethoscope instead of the diaphragm. The bell is used for low pitch sounds like blood pressure and bowel sounds. The diaphragm is used for high pitch sounds like breath sounds.
In a moving vehicle, people have recommended putting your feet on the gurney, and don't let the patient rest their arm on the gaurd rail.
If you put the diaphragm/bell under the cuff, you might hear a lot of extraneous sounds side as the vehicle moving. It can also cause the patient unnecessary discomfort.
Also when you are listening, you could try closing your mouth. I think mycrofft mentioned that on another blood pressure post, and he was talking about how if you stick your fingers in your ears while your mouth is open, and then you closed it, you can feel it narrow. Dunno if he was just seeing if we would be dumb enough do it or not, haha! I think it makes sense. ^_^
I would link you to several other good blood pressure post, but my searching skills failed me. We had one massive one, but the problem is, trying to search "blood pressure" in EMTLife gives you just about every post, haha! We do have other good posts though so definitely search around. There was one really massive one that had a bunch of goodies in it that I think I mostly covered. One good one on how to do it, one one NIBP v. manual, and then JPINFV wrote a little thing that included about taking into consideration of what the machine says....
Good luck.