The Elder Scrolls Online

Have fun. Find out what you like doing and do it. It's a big game, there's something for you if you had ANY interest in playing in the first place.
Always research traits, for every type of crafting. There is NO EXCUSE not to. Even if you swear you won't craft, just do it. It's basically free (OK, you didn't sell one item, so what) and if you decide to start crafting later, you'll have a HUGE leg up on other late-bloomers.
Loot everything up until level 5 or so, including Coldharbour (for those aforementioned motifs and provisioning recipes). After level 5 or so, food ingredients and "trash loot" become less gold/space efficient and you can start ignoring them.
Always loot: Chests, trunks, wardrobes, desks, bookshelves (skill ups!), other furnishings. These can drop racial motifs, which people will pay for. You can always drop the "junk" you don't want, like crafting materials, and such, but it's worth going through them for motifs, lockpicks, and treasure maps.
Save up for the 43,000 gold mount, it's strictly better, and you can make it a few more levels without the 14,000 gold one (the Imperial one, if you have access, is a good buy).
Go back to the starter islands, even if you blow through them. There are at least two skill points each (including skyshards), decent loot, achievements, and lore books to obtain. On that last note of lore books, go join the Fighter's, Mage's and Undaunted guilds BEFORE going back so you can work on advancing those along the way.
If you encounter a bugged quest, and others seem to be having the same issue, it's likely caused by a phasing issue, and the quest triggers are overloaded due to multiple inputs at once. The best way to fix this is to leave the area and come back later and/or log out WAIT 5 MIN and log back in. This was advice given to me by in-game GMs. That being said, they claimed to have fixed most of these issues. The big problem is that everyone stuck has to do this to reset the triggers, so please cooperate if you find this happening to people.
READ THE QUEST TEXT! If you haphazardly click through quest text you will often be lost on what to do. This is especially true in puzzle quests. They tell you what to do, but they don't always keep that information in your Journal, so if you spam through a quest's dialogue and then you have no idea what to do you have only yourself to blame.
When not doing seriously difficult content, pop on one of each armor type for easy skill ups in case you wish to change types later. I wished I did this during the beta.
You can level weapons/armors that you're not wearing if you have a skill for that line on your bar. You won't be able to use the skill, but it will count for leveling the skill line.
For general questing, have a "action bar" and a "skills I want to level up" bar that you swap to when turning in a quest. This is especially useful once you've caped a skill at tier 4 of a morph and it's a "wasted" slot when it comes to XP.
Eat food and use your potions, you'll get enough of both and they really help, and the basic ones (at least) drop often enough that you shouldn't be shy in their usage.
Discover all the weyshrines asap. Divert your course to find them. They'll help you to no end.
Want to leave Cyrodiil? WEYSHRINE (Not transitus stone)! There are two weysrhines per faction, at the "home bases". Although I suspect that, at launch, you can simply walk out, but don't quote me).
Soul Magic is worth leveling up, get that skill up to one of the morph rank 4s asap, there' no reason not to level it at low levels, and then you're set. Soul Gems are worth having and relatively easy to obtain.
Don't forget to repair your gear, it really makes a difference. Check if you can repair at every vendor and do it.
Pick up every quest you come near, even if you don't want to do it. You don't have to, but there is often lots of overlap so you can end up inadvertently completing two quests and getting some bonus XP (or even a skill point).
Search out mundus stones, their benefits are very much worth having.
I'm sure I could ocme up with more, but that's just a little bit to help you get started.

GENERAL RULES OF THUMB

• You will level slightly faster if you go pure dps, but you will have a harder time getting into pick-up-groups since pure dps is dime-a-dozen
• If you want to tank or heal a 4-man, know what you are doing; do not queue for one unless you are competent and are geared/skilled for it, otherwise you waste your and everyone else's time
• Go nowhere without at least 10 lock picks on you (my preference is 20); buy more if you have to; always unlock chests, even if you have to break all your lock picks figuring out how
• Do not follow any set path; run in any direction your heart desires, except where I note below
• Always pick up all quests you see when you see them; no need to do them as you pick them up
• Kill everything you pass
• Loot everything always
• Harvest every node you pass
• If your bags get full, head to town, sell junk and working on crafting
• Avoid paying for a teleport if you can avoid it; sometimes even suiciding by /stuck is better than paying for a port since repairs are very cheap early on; try to always jump from Wayshrine to Wayshrine for free
• Before leaving town, dump everything from your bags into the bank except quest items, gear, food and lock picks
• If your bank gets too full, bring another character online, get it directly to a bank and extract a set inventory type (ores, woods, food reagents) to that one character; it will now be your "master of ores" or "master of woods" or whatever; this will give you a massive inventory, no longer limited by your bank size, that will come handy as you level your main; you can also mail things between characters as needed, although I never actually tried that in beta

BEGINNING

• Create eight characters with names you like as fast as you possibly can, disregarding anything about them but their name; you don't have to keep them; they are placeholders and temporary bank extensions
• Pick one of the eight to be your main and delete them; then rebuild them, taking great care to make them just the way you like, keeping the name of course; this will be your main or first main
• While working through Coldharbour, loot everything you can for recipes/ingredients; do not be in a hurry to leave
• Once you can make it to town, check the horse situation; if you can afford one, get it and feed it its first apple (IMHO, the other foods are worthless)
• Level up your provisioning as high as you can
• If you have a research slot available in any of the professions, and it won't destroy a piece of gear you need, begin researching; you can have one in each profession going at the same time at this point
• Crush any gear/weapons that you don't need for their raw mats
• Toss everything except needed quest items, gear, food and lock picks into the bank; buy more lock picks if you need to
• Eat a food buff then head out to work on the starter islands
• On the starter islands, do everything, skip nothing; get all Skyshards

MAINLAND

• Do every public dungeon you stumble across; many of them have a Skyshard (be on the lookout)
• Feel free to wander and do pick up every quest you see when you see it; you can always come back later
• Always be on the lookout for Skyshards... look up, down, all around, they can sometimes be hidden
• If you hear a Dark Portal open up, drop everything and go there
• If a Dark Fissure opens on top of you, kill everything you can, waiting for help if you need it; you can wash the "scared the shit out of me" poo out of your underwear after
• If you are near a world boss and see other people begin attacking, join in
• Basically rinse and repeat things I wrote above as they are applicable

CYRODIIL

• If you are into PvP, head there at 10; do the quests; kill enemies; win
• If you are not into PvP, head there anyway and explore; there are Skyshards all over, including in public dungeons; you will get killed, it's okay
• If you can manage it, go there in a group, even if only to farm for Skyshards