Leveling your Character
Levelling up your character in Elder Scrolls Online is a smooth process, though the focus on how fast to do it changes on if this is your first or second character.
Your character level is divided (confusingly) into two systems. All characters must level from L1 to L50. The Champion System starts after this from CP1-160 and onwards up to a cap of CPX
As you roam around the world you are "Battle Levelled" meaning the game treats you as a higher levelled character, meaning that monsters you face, even if questing with higher levelled friends, should not overwhelm you. However, this can make the game suddenly seem harder once you reach L50 (so practice your combat and be prepared).
After you reach Level 50, you then start earning Champion Points instead. Champion points can be spent on "perks" under the Champion System that can make your time in ESO a little easier. While there are combat focused perks, there are also perks that do things like increase harvesting speed or give you a chance of better gear from opening chests. There are many guides around as to how to spend your CP in a way that best helps you in your play-style.
Champion points have another advantage in that you only need to earn them once. All characters need to level on their own from 1 to 50, but once they pass L50 they immediately jump to your full Champion Point level and all experience earned on CP characters contributes to your total CP. This makes it easier to level multiple characters.
Level = Character Based | Champion Points = Account Based
Leveling Skill Lines
In addition to your character level, each skill line must be leveled from 1 to 50 to unlock skills and passive abilities associated with that skill line. Most skill lines are unlocked by simply using the skill or having it on your skill-bar when turning in quests. This includes all class skills and all weapons skills.
Other skill lines are progressed by doing the quests associated with that line. These include the Psijiic line, the Thieves Guild and Dark Brotherhood lines.
The Mages Guild is leveled by finding an reading lore books (actual reading of the text of the lore books not required, but it is recommended). MAKE SURE you go to the Mages Guild straight away and join, otherwise the books don't count.
The Fighter's Guild is leveled buy killing undead and daedra. Unlock both the Fighter's Guild and Mages Guild as soon as possible to take advantage of your normal progress through the world. MAKE SURE you join the Fighter's Guild straight away, otherwise the kills don't count.
The Undaunted line is leveled buy joining the Undaunted Guild at L48 (look for an in-game mail with details) and then completing daily dungeon quests (pledges) and dungeon and trial achievements.
Leveling Individual Skills
Individual skills must also be leveled. Using the skill or having it on your bar when you turn in quests is the only way to level a skill. Once a skill is leveled to Rank 4, you're given the choice of two morphs, further allowing you to customise your character build. Often a skill morph might switch a skill from a magica focused skill to a stamina one, or from a short ranged skill to a long ranged one.
Skills require Skill Points to unlock. Skill points are granted by leveling your character from L1-50, the main quest through each zone, finding skyshards in the world, leveling PvP ranks, doing the story quests in dungeons and other places.
If you're new or returning to ESO, do turn on the Skill Advisor which will give you a selection of recommended skills on morphs that can guide you until you feel confident in your own skill selection.
There are also a number of very helpful player run sites with extensive build guides that you can pick and choose from, but the Skill Advisor will get you started.
Your crafting skills are leveled separately to your combat skills. If you plan to play ESO for some time you should absolutely level these skills as well; it will save you money and allow you to improve your own gear.
Level Blacksmithing, Clothing, Woodworking, Enchanting and Jewellery lines by deconstructing items dropped in the world. Level Alchemy and Cooking skill lines by creating potions and food.
You can also level all these skills by doing the daily crafting quests called Writs.
WAYS TO LEVEL
Take your time if you're new
If this is your first character in ESO, don't rush! Take your time, enjoy the game, enjoy the world. Start in your starting zone and follow the quest line. Then move to your Alliance starting zone (Bleakrock for Ebonheart Pact, X for the Aldmri Dominion and X for the Daggerfall Covenant) and follow the main quest line there (use the Zone Guide accessed with the map to help you find your way). You will pick up skill points and armour in the "training" trait which will level your skills more efficiently.
Level skills quickly
When you turn in quests, make sure the skills you wish to level are on the active bar; this will give these skills a bigger boost. If there is a particular skill line you wish to level (rather than just an individual skill) put multiple skills on your bar.
If you're on PC/Mac there are add-ons that you can use to switch between sets of skills quickly which makes this process less annoying.
Level with a friend
If you can find someone to run around with, you actually receive more XP than on your own. If you can find a friend with a high level character this is even faster! You can even marry another character in the game, and if you're questing in the same group you gain another 10% XP.
Note, you don't actually have to be grouped for this to occur, if there's one other person around and you're both killing mobs you should both get the benefit. Once there are 3 people in the group however the gains drop.
Grinding is where you repeatedly kill fast spawning mobs (monsters) in a small area. This can be an efficient, if tedious, way to level (but it doesn't get you additional skill points from quests or skyshards).
Make sure you're killing undead and you'll also be leveling your Fighter's Guild skill-line.
Rather thank killing mobs in the world you can kill the mobs that spawn at Dolmens (Dark Anchors). This can be a good way for very low level characters to get XP and the Fighter's Guild line. Alik'r almost always has several big fluctuating groups rushing from Dolmen to Dolmen.
This will also give you gear (including Jewellery) to deconstruct. Watch zone chat for the command to type to automatically join a group and just follow the leader.
XP Scrolls and Potions
Daily login rewards often include 50% extra, 100% extra and 1050% extra XP Scrolls, which last for 2 hours. You can also buy XP Pots from other players (which can be crafted from items in the game). Use these to increase the speed at which you level.
There are multiple events during the year which also have an XP bonus while you're participating. The scroll and event bonuses stack, which can make levelling even faster.