Non-atmospheric planetary landings are now part of Elite Dangerous and it's an interesting process to land on one. It's essentially three phases. You're either in space itself, within the gravity well of the planet, or near the surface. Since these are non-atmospheric planets, they still have gravity, and therefore your ship will be "dragged down" but due to some interesting video game mechanics, your lateral thrusters will fire to keep you stationary and compensate for the gravity. Ship flight while within a planet's gravity well remains the same as if you're within space, minus the fact that there is a very hard rocky surface under your ship that if you hit with any speed above "landing" you're to likely either take severe damage or crash.

You'll need a planetary landings outfit purchased at any station (mine was already on my ship) and if you want an SRV, you'll need to use one of your extra accessory slots to equip one. Go ahead and do that before you fly to a planet.

Approaching a Planet

First things first, you need a planet to land on. I suggest looking for outposts that are located on a planet on your radar. That's going to get you the closest planet you could probably find easily enough. Any planet without an atmosphere can be landed on, with a few exceptions. Generally any planet that has an outpost on it is notable enough for you to want to land on (outposts on planets have planet related missions). You'll then need to obviously set course and supercruise there.

When you get close to the planet, throttle down or you'll obviously hit the too fast warning. At this point you'll enter into the planet's gravity well, and you'll get a "PFD" or primary flight display like system showing up in your hud to let you know where your ship is in relation to the ground (sort of like flying an airplane). At this point, you'll see a yellow line circling around the planet. This is where your supercruise will turn into a glide (assuming you're not going too fast) to help you on the last leg of your journey to the ground. Once your glide is finished, you'll then be at normal speeds, and can proceed to land, either at an outpost or anywhere you can find some solid ground.

Landing

Landing is the same process as anywhere else, except unless it's an outpost, you can land anywhere there is flat ground. To land on the planet, simply approach the ground and using your verticle thrusters (up and down). Your HUD will display if the alignment is fine or not (if the ground isn't flat enough, you won't be allowed to land). Assuming you have the all clear, proceed to set yourself down slowly, very, very, very slowly. Then you'll attach and have landed. Outside of an outpost, the only thing landing accomplishes is access to launching your SRV, which is handy if you have a mission and need to exit out of your SRV to take care of it, but it's several KM away.

SRV

To launch your SRV, look down and then click deploy (assuming you have one loaded up). Once out in your SRV, you can have your ship takeoff (which is useful if you're going a distance, as you can get your ship back to you faster) through the same menu. You can also have your ship return and land near you on the same menu, so that you can easily take off again. If your SRV is destroyed, you'll return to your ship. Once your ship is dismissed, either from going too far from it or choosing to dismiss it yourself, it'll enter low-orbit mode where, I'm 99% sure it despawns and you don't have to worry about it until you call it back down.

While in the SRV you can use the lasers shooting forward, or enter turret mode where you can drive but use a 360 degree turret that is disconnected from the movement (meaning you can look around and fire anywhere, while driving around).

Taking Off

To take off from landed, simply engage your verticle thrusters for long enough for the ship to take off, then enter supercruise. At this point, it'll want you to align with your escape point and then voila, you're back to cruising around the planet.

That's pretty much all there is to Elite Dangerous's ship landings on planets. You can exit your SRV while in an outpost or on your ship and all of the games mechanics work the same. The only thing you have to be aware of is that the planet's surface WILL cause damage. You WILL take damage if you ram into the planet's surface.