You can purchase items from a guild owned vendor (there is no central AH), however if you wish to sell your items to other players you must belong to a trading guild (a guild that has a trading kiosk. These are bid for by the guilds themselves.)
You can belong to up to 5 different guilds at the same time. Not all are trading guilds. I would suggest checking the Guild Recruitment forums for those recruiting or ask in general chat in game. Enjoy your stay!

You can ask in in-game chat for an invitation to an active trading guild. Make sure you specify whether you are interesting/willing to pay dues. There are no-dues guilds and weekly/monthly-dues guilds. The latter typically charge 3K-5K per week to maintain trader access.

At first, I recommend you join a dues-free guild or two. Once you've been playing for a while, and able to generate, say, 50K-100K sales per week from your traders, you won't care about the dues, but will want to pay for the benefit of a more reliable trader. dues-free guilds tend to lose their traders a good fraction (like half) of the time because they don't have enough gold to make strong bids for their trader every week.

Once you're in a guild, you can post items for sale in the guild store. If they have a trader that week, the whole ESO community can wander by and shop at it. If not, then only your fellow guild members will have access to buy for that week. You may still make some sales; most such guilds actively promote buying from within the guild if possible.

Once you've got items posted in a guild store with an active trader, you will still have to figure out how to price things so that you can profit and still move merchandise at a reasonable rate. For the kinds of things you sell, you'll eventually know how to price it to move (a) within hours or (b) within days or (c) maybe by the end of the month when the listing expires. Of course, the longer you're willing to wait, the more you can make on an item. But volume can be more important than markup, especially if you're a master crafter of some kind. I'd much rather sell 10 potions for 100 gold profit each than 1 potion for 200 gold.

Also until you get into a guild you can try and sell some stuff in zone chat. Do a little checking on prices though so you don't let something go for less than it is worth. Don't spam chat to much though and ignore the inevitable trolls that seem to always pop up.

I've got one just for new players Send a PSN to Heathenpride and I'll add you gladly. We have 220+ members so far and we have around a dozen launch day players on hand to assist