Regarding keystones, think of them as the “difficulty setting” of the dungeon. When advertised in the groupfinder, the number indicates the difficulty the group are planning to run the dungeon at (which means at least one person in the group, usually the group creator, possesses a key of that level)
You do not need a key of say level 4 to participate in a +4 dungeon. You simply need to join a group where someone has a level 4 key, which the groupfinder will typically tell you (such groups will advertise as +4)
However, it is extremely typical for people to expect you have experience in the dungeon difficulty or thereabouts when considering whether you should be able to join, so although you don’t need a +4 key yourself, people will usually expect you to have experience running a lot of +2 and +3 before they’ll let you join a +4.
You can of course use your own key and make a group. This way youre the one setting the difficulty and thus you decide who comes into your group or not. This is one way to get experience in those keys.
So let’s use your +2 key as an example. You could make a group for this keystone and place it in groupfinder advertised as +2. Start a group and run the dungeon.
All dungeons at +2 or higher have a timer. If you beat the timer, whoever used their key to trigger the dungeon has their keystone upgraded. The quicker you complete the dungeon under timer, the bigger the upgrade (maximum of 3 levels upgrade).
So if you just about manage to time the dungeon, you’ll get a random +3 key at the end which you can use to make another group.
If you time it with a minute or two spare typically, you’d get a +4 key instead.
If you complete it even quicker than this, you’d get a +5 key.
So the way to progress to participate in higher keys beyond your own is to either use your own key to gather experience or join low keys of other groups where they won’t ask for excessive experience.
For example despite my example earlier, most sensible +2 and +3 groups aren’t going to expect you to have tons of experience running times versions of dungeons before. This is because the timer is usually easy to hit at these dungeon levels and the additional difficulty isn’t massively different in changing how the dungeon is dealt with (either the boss or mobs will simply have more health).
At +2, and then again at +4, +7 and +10, you get new “affixes” that are attached to the dungeon, changing what you need to deal with. This could be stuff like Bursting (killing a mob makes the party take a DoT which stacks) or Bolstering (killing a mob causes nearby living mobs to get a permanent damage and health buff). These change how you deal with the dungeon as they may make it so you have to kill mobs in a certain way to avoid the affixes overwhelming the group.
As said, the +2 affixes (Tyrannical or Fortified) don’t really change what you need to do in the lower key range, they simply make the boss or mobs have more health and damage. So experience in dealing with them isn’t necessary.
With the others, unless your group overhears the dungeon, if you do not “play around” the affix you will very likely wipe/not time the dungeon.
For example with Bolstering typically you’ll either cleave the mobs so they all die together (so none are buffed) or in packs with a lot of non elite trash and an elite mob or two, you kill the elites first otherwise the trash deaths would buff them and make them extremely difficult to kill, which is contrary to how you’d usually handle such a pack (usually your cleave would just kill all the trash quickly whilst you focus on the elites).
Because these affixes change the way you play and require a bit more management to beat the timer (if you keep letting mobs bolster for example, they take ages to die which means beating the timer becomes hard as you can have a normal elite mob taking upwards of a minute to kill depending on their stacks) so people aren’t so quick to invite you into keys at 4 or higher unless you can show you have experience timing keys in the levels just below.
I hope this post makes sense, apologies for length
Edit: I forget to add if you’re newish to the mythic plus scene and interested in trying it out, there are a few communities on either factions that specifically aim to create more chilled environments for people playing and learning mythic plus. These communities will form groups from “in house” and typically won’t ask you to have the experience a groupfinder group may when letting you in, as their philosophy is about helping people learn via direct experience. Consider looking them up for a good starting point to get some initial groups under your belt. Scared of Dungeons is the biggest Alliance one and Zen Horde is the horde equivapent.