First off sorry for the long post and I'm far from an expert or even a good jumper so take this with a grain of salt but these are some of the things I've learned over the years trying to jump.
First learn how to do a really good bunny hop, not the pull both wheels up at the same time bunny hop but like a trials riders would do. The motion is almost the same just way less exaggerated since the jump will do most of the work for you. If the jump has a good transition/lip it will feel almost effortless much like how it looks in the videos of really good dirt jumper bmx kids. So watch how trials guys bunny hop...they load the bike (like how you push into and pump a transition, this motion and the next part is also a bit like how you start a manual)....pull the front up (like coming off the lip)....and push through and level out (like when you're in the air) and look towards the landing.
Check this out for a side view of this jump:
http://leelikesbikes.com/Stories/102103/
And around 45sec in on this bunny hop video and compare how they look:
Looks almost the same right?
So first focus on the approach...look to and be ready to pump/press into the transition in the "attack" position...knees and arms bent...
...push down through your bike as you're hitting the transition....the timing when you do this varies with the size/shape of the jumps transition and takes practice to learn....as you're going up the transition you're looking at the lip getting ready to time when to unload/pop off the lip...this also takes much practice to learn when to do it....if you time this wrong or do nothing and let your weight get pushed into the bars here you will often get kicked forward into the endo position and most likely crash. Again if you're doing/timing it right it will feel almost effortless.
Above all if you are not ready heading into the transition/jump and don't feel things are right STOP! Messing about heading into a jump i.e. trying to throw and extra crank or two in, shifting gears or moving you feet/hands around is a sure way to come off the lip out of balance and or throw your timing off and end up dead sailor/crashing. When you first learn to jump it's difficult to throw/get away from the bike since you're not going very high so just abort things before hitting the jump and try again. And don't be afraid to ditch the bike if you can! I love my bike but it its me or the bike I'm going to choose me over the bike or a broken bone every time!
You can also almost visualize a jump like pumping up and over a big roller....except the top part of the roller you're pumping up and over is cut off/invisible (so the part where you are in the air) if that makes any sense. So you can imagine its just a big mound of dirt under him instead of a double and he's just pumping up and over it to kinda see what I mean:
Once in the air
LOOK TOWARDS AND INTO THE LANDING like you can see in the photo not down at the gap or your bike! If you look at the lip you'll probably case it. You can see in the photo above the riders front wheel will land a bit down the landing transition and the rear wheel will land near the top ready to pump for the next jump. This was/is still the hardest part for me...my front wheel lands at the top where my rear wheel should have and I will case the jump nine times out of ten LOL.
The other thing I learned when landing is to have front end, your bars, head and shoulders square and pointing in the direction you want to land. Head leads body follows. So the back end of the bike will just follow like a trailer even it it lands at an angle as long a the front end/your head is going in the right direction. It seems scary at first if the back end hanging out a bit when you land but don't worry about it much. If the front is coming in at any weird angles though you're probably going to crash so don't do that. This also usually starts all the way back at the beginning because you're stiff/unsure/unready heading into or coming off the lip.
So stay loose and relaxed in the air don't worry or be afraid if the bike moves around, sometimes tweaking the bike a bit helps to stay loose. If things are feeling off or you are tired stop as well...the I'll try just one more usually ends in disaster...don't ask me or the ribs I broke how I know LOL. Watching dirt jumping POV's helps too with visualizing the timing and flow of all of this from the riders perspective.
And hook up with some friends/riders and take a weekend trip out to Ray's Mtb Park in Ohio over the winter if you can its well worth the drive and a great way to learn. They have a huge variety of table top jumps in all sizes to learn on and a huge foam pit. There also wood jumps so perfect smooth transitions, dirt jump transitions can be pretty sketchy at times. And if you're not feeling the jumps one day just riding there is a blast even without the jumps. You could also bring the family and make a trip out of it there's also plenty other fun stuff like the Rock and Roll Hall of Fame and Science museum IMAX theater, the house from A Christmas Story etc...