Surface swimming with mono is a bit tricky in the beginning. First of all, you need a snorkel, preferably a front mounted one. Finswimmers swim a bit like leisurely cruising dolphins: large kick with almost straight legs, stiff ankles to facilitate the upkick, large hip movement. After every downkick there's a short dive, then upkick a bit under water. After that you surface, clear the snorkel, breathe and start again with a downkick and dive. It takes some practise to make this work, and you really should see how the finswimmers do it. It might be easier to start with two kicks / breathing cycle (like swimming butterfly), one for the dive, one for surfacing.
According to finswimming rules some part of the swimmer has to be above the surface all the time in the surface events (snorkel is part of the swimmer), so the "dive" is not a deep one. Of course there's no need to abide by the rules if one is not competing, but this might explain what you see while watching finswimmers practise, i.e. why they do not dive a bit deeper and do a couple of kicks underwater and then breathe.
Arms are at all times extended, hand over hand, wrist over wrist, head well tucked between arms, so that ears just touch or are below biceps. You probably need a nose plug to comfortably keep your head on proper position.
Finswimmers do not use monofins all the time as the foot pockets tend to be too tight to be worn for extended periods and monoswimming with correct form is quite tiring. They do lots of reps with plain old rubber bi-fins between the mono-sets, so that might be a good idea for a beginner to practise the technique.
If your lower back and abdominal muscles get sore, then you are probably doing something right, since it's the strong core muscles that should work the hardest; in dynamic apnea there should be much less lactic acid caused burn in the legs when using a monofin / dolphin kick as compared to using bi-fins and flutter kick.
All that said, I'm not a finswimmer myself and certainly not very qualified to give advice on swimming technique. Try to get into a contact with some finswimmers.
ossi