I played in PTS since August last year, and these are a few tips I gathered on the way. Please do check also the more comprehensive lists in the Links post from Lateralus.
The first skill points should be allocated one in each of the three trees of the class you selected, and one in the first weapon selection. Keep one of each skill tree + one of the weapon skills on the bar always - this will ensure you level all of them up.
Do the same for armor: wear a combination of the heavy/medium/light armor, if you intend to level more than one type of armor (and it is generally a good idea to combine 2 of the three).
Collect all skyshards in each zone, 3 skyshards = 1 skill point. And you will be starved for skill points when you start.
You can get a list of skyshards and hints for each zone under Achievements/Skyshards (press J and select the Achievements tab from upper right buttons). If you have trouble finding one check online maps (google for ESO maps).
Learn to read what the enemy is doing and take appropriate action: dodge/block/interrupt are important. The enemy animation will give you a hint of what is comming. For example: red circle/cone on the ground = dodge.
Past level 6 buy a few soul gems of the appropriate type (petty to start with) and use the soul trap skill to fill them - they are very useful when you die, unless you enjoy running from the nearest shrine. Also used to recharge enchanted weapons. To charge a weapon right-click it in inventory and select Charge.
When you get to levels 10/20/30/40/50 buy the appropriate type of soul gem, slot the soul trap and get to and area with same level monsters and fill in about 5-10 gems. You can still use the lower soul gems to recharge enchanted weapons.
Loot everything, gather all resources. Crafters will pay/love you for it.
Make a few alts even if you do not intend to play them - they can be very useful mules at 60 inventory slots each. Place them in the starting city at the bank. Highly recommended for crafters.
Bank is shared among characters, use it as a transfer buffer. To craft you need mats either on you or in the bank.
Crafting is useful, but can get expensive in terms of skill points (especially in the early levels). Consider creating and leveling 2 alts to about level 10-15 for leveling Provisioning and Alchemy only. These two crafts are easy to level and very useful, and can be raised to 50 with only a handful of skill points. Your main should level the rest of the crafts (or the ones you wish to pursue).
You can share and accept shared [some] quests in a group.
Options and keybinds:
I enabled Autoloot and area loot, and use a small addon I wrote to display all I looted in chat.
Bind autorun to a key, it is helpful to watch the map and run at the same time (but you may miss chests/resources, run into monsters, so use with care).
You can break out of CC using the Interrupt (by default = Left+Right mouse click). I found it somewhat unreliable so I bound it also to a key.
Addons I used and found useful:
- FTC (may need some manual tweaking to work)
- mini-map
- loot display addon (there are a few available, try them out)
AvA
Do not skip the starter quest: it gets you alliance points as well as familiarity with siege engines and a limited use camp (nice to have).
Accept all quests, you can always drop them, if your group does another objective.
Hope this is useful, please add if you have more.