You can do them from the SRV or from the ship (if you have a small or some of the medium ships). SRV might be easier for the undefended or less defended data points, ship dfinitely is easier for the harder to access or better defended datapoints, as in some cases the data points you need to scan are locked away behind barriers which you may need to disable first (or find some other way around).
SRV:
- you need Horizons (assume you got it, otherwise you shouldn't see the planetary missions. Otherwise, wait a couple of weeks - Horizons will be merged into the base game on the 27th)
- find a station that will sell you a Planetary Vehicle Hangar. They come in size 2, 4, and 6 in G and H varieties, so make sure you look for them after having selected an appropriate slot. G has less mass, needs more power and is more expensive.
- after you've installed the hangar, you will have to buy SRVs for the hangar's slots (1, 2 or 4). The hangar doesn't come equipped with vehicles. If you lose an SRV, you can restock them on any station that offers restock, no need to find an outfitter
- then you'll need to map (or, at least, check) your key binds and firegroups. SRV key binds are seperate (for the most cases) from ship keybinds. I just hope that there are SRV tutorials now available from the start menu.
- same goes for planetary landings - look for tutorials in the start menu
- otherwise, you'll need the planetary landing suite installed on your ship (it comes as default. I think you can sell it, but as you can't install anything else in that slot, that's pretty pointless).
Landing:
For starters, select a nice smooth-ish low gravity (less than 0.2 g) landable moon, and equip your ship with shields just in case (who am I kiding?) you botch the landing

. Select the moon from your nav panel, and approach it like you would approch any other target in SC. Throttle down to 75% when at 8..6 seconds ETA, then throttle down to 50% when the moon changes from a point of light to an actual sphere. You should now approach at ~9 seconds ETA, speed dropping.
Aim for a point on the horizon.
On the left side of your HUD, you have a target display. It should show the planet and a distance and speed indicator. The speed indicator has a blue zone and will show underneath your speed as ">215 km/s". These 215 km/s are the highestr speed at which you should enter Orbital Cruise. As you apporach with 50% throttle, your speed will drop. At some distance from the planet, some new HUD indicators will pop up, indicating the distance to the surface (for now) and the OC drop point. When you hit that point, your speed should be "in the blue", i.e. below 215 km/s.
One you hit the OC boundary, your HUD will switch to Orbital Cruise mode: the target indicators on the left will disappear and your main HUD will now show a compass (on top, horizontal), a inclinometer/artificial horizon, the height indictor will change to show the glide drop height and you'll get a variometer (height change indicator) on the right. Bleed off your speed at constant height until it doesn't change any more (for me, that's usually 115 km/s at OC drop height and 50% throttle - the lower you go, the lower your speed should be).
Now you're flying at a constant speed in Orbital Cruise - but you wanted to land, so you need to get down.
Push the nose down.
You will see different colours in your artificial horizon: blue around the middle, then orange and, if you go down further, red. Stay out of the red. Int the blue zone, your speed will increase up to cruise speed for that height and throttle setting - good if you wnat to get to a specific spot on the surface. For now, just tilt down to about 40°. Your speed will drop smoothly with decreasing height (in most cases) untiol you reach glide speed (2.5 km/s) at the glide drop point, where you will be dropped into glide mode.
Glide isn't supercruise any more, so any hard maneuvers will have you drop unconscious from the g forces - avoid them for now. Just go down at your constant 2500 m/s and 40° angle. You will be dropped out of glide and into normal flight at ~7 km height over the surface at that point (some planets/moons have mountains and ravines larger than that...).
Ok, now you can change the throttle again - to whatever you like. Just keep in mind that, for all ships to a greater or lesser degree, the only thrusters that can keep your ship up are
- belly (ventral) thrusters
- main (rear) thrusters
Depending on the local gravity and your ship, the other thrusters may or may not be able to keep you up. So if you tilt your ship down or roll to either side, you might go down more or less rapidly or heat up rapidly. If in doubt, just keep her nice and horizontal. At 0.2 g's or less, that shouldn't be much of a problem, though.
If you want to land, fly down to maybe 100...20 meters and deploy your landing gears. Your radar will change to ground view. Now you should have the lateral thrusters mapped to some controls, and for preference the vertical thrusters to an analogue control. Hover over the surface and look for a suitable landing spot. The disc under your ship on the radar will turn blue when you can land there. Then use your vertical thrusters and go down gently. Analogue controls will let you do the "gently" part. Again, with a well shielded ship on a low g planet, that's not a big issue.
Coming in too fast with an explorer build on a high g world, however...