If the car's jumping, you're probably coming off the clutch too quickly or not applying enough gas.
If the car starts to slow down, you've probably not added enough gas, or you may be in too low a gear if you just wish to cruise on minimal power.
I usually bring it up sharply to the biting point (because I'm incredibly familiar with where that is on my car) and apply throttle ever so slightly, then bring the clutch up the rest of the way. I don't go past the biting point without a touch a throttle, but it only takes a little bit for the gear to change successfully. If you don't have enough gas, the car might start to slow down under engine braking, so just add a little bit. You can see this while stopped by pressing the throttle just a tad and watching the revs go up.
Note: I don't pause at any stage of this, with practice you'll be able to time it all into one fluid motion. You can move both feet at a slightly different speed because your brain has been trained to change gears.
The bit between fully releasing the clutch and adding the power is a grey area. On lower gears you may have to be a little gentler so you don't spin the wheels or zoom off, but higher gears can usually take greater throttle input whilst changing gears because those gears are less powerful. It's really down to experience from there.