There's a number of things you can do in ESO as a low-level player in Cyrodiil.
Firstly, you can participate in various forms of PvE content throughout the zone. NPCs are all level 50, but the game does scale your stats to 50 as well, so you'll be able to fare okay. There are a number of dungeons, PvE quests, Skyshards, etc. in Cyrodiil to keep you busy, if you find you're not doing well in PvP right now.
Secondly, you can try to find a group of other players to join. There are usually groups of some sort advertising in Cyrodiil, and having other players to back you up can help even the odds in PvP, or even tip them heavily in your favor.
If you don't want to find a proper group to join, you can also try joining in on a siege. Whether defending or attacking, there will be plenty of players on each side of the conflict, and so plenty of support/buff/heal abilities being thrown around if you need them. The larger number of players also can make it less likely you'll personally be targeted, assuming your side is greater in number.
If you really do want to solo PvP in the zone, there's still a few options. The simplest is to leave for a few levels and come back; at level 15, you gain access to the weapon swap mechanic, and with it you also get a whole second bar of abilities to use. This one mechanic alone can make a huge difference in the performance of some builds. Also, in the early levels, you probably haven't got all your abilities morphed yet; holding off for a few more levels to get some of those upgraded (especially if you're going for morphs on abilities that add healing) can have a big impact.
You should look into improving your ability to sneak. If you're a Bosmer or Khajiit, or using Medium Armor, there are passive abilities in those skills which can help. Even without them, just learning to be aware of your surroundings, learning how close you can get before enemies see you, etc. are very useful in helping you get across Cyrodiil without trouble. A useful tactic is, upon entering sneak mode because there are enemies nearby, wait until you go undetected, then walk away from where you were in a somewhat random direction. Even if an enemy spotted you and heads to where they last saw you, you've since vanished, and it's generally not worth their time to hunt a lone player down.
Lastly, if all of the above isn't enough, you can try switching Campaign. Some of the campaigns can have lop-sided player populations, and if your own alliance is more populous in one campaign, that can translate into an easier experience while you get used to Cyrodiil and ESO PvP in general. You can either switch your Home Campaign, or just enter another one as a guest to get the hang of things. Just look at the little cell-phone-signal-bars icons in the list of campaigns to see how many people from each alliance are in a given campaign.
Best Answer
While Bunyip's answer is basically correct, it isn't 100% complete:
You can't enter other alliances' territory through Cyrodiil.
The gates leading to their provinces (High Rock, Morrowind, and Elsweyr) are considered safe zones where players can spawn, organize etc. They're walled off (with one way doors back only usable by the owning alliance) and heavily guarded as well.
Once you've reached level 50 and completed your main quest storyline as well as your alliance's storyline, you'll be presented with the option to play one of the other remaining alliances as veteran content (often referred to as 50+).
This will allow you to play all of that chosen alliance's content with your existing character while having everything upscaled to level 50 (so it's still challenging and you're not just breezing through heaps of low level enemies).
Once you've finished your second alliance playthrough as well, you'll be presented with the option to play the last remaining alliance's content as 50++ which will once again allow you to enjoy the content with raised level/difficulty to accomodate your more experienced character.
As a side note: I haven't heard of any rumors changing this, simply because of the fact that it wouldn't fit well with the storylines (and the content is accessible already). Take the Ebonheart Pact storyline as an example. Without spoiling anything significant, it starts off with an invasion of Daggerfall Covenant forces in Skyrim and Morrowind. Why would they allow any member of the Daggerfall Covenant to join their ranks driving them back? This doesn't make any sense.