When I first logged in to TSOS I know I was a little confused, and wasn't really sure what to do. As with now, the people around were friendly and very willing to help me out. So now it's time to pass on some experience. This is a broad overview of some key things to keep in mind. For more specifics you'll have to ask other players.
First off, figure out what type of character you are interested in playing. Get a general idea of if they are a fighter, or a channeler, or whatever. The next thing to do is to go through creation and set up your character. Choose a name that is suitable, so not from the books, or pop media, etc. Go through and choose nationality, appearance, and talents according to what you want your character to be like. For attributes, I've always found that Phys, Agil, Inte, and Perc are the most helpful. Once you are done with creation, you enter the intro area. There is some information here about the setting, make sure to read all of it if you need a brush up on your Wheel of Time.
Once you have been authorized, head south to enter the main world of the game. It is now time to start the game for real. Remember that the fastest way to both power and having fun on tsos is to RP with other players. Chat is an ooc channel, and a great way to get questions answered by whoever is on. To find out who else is online, type who. There's not really any way to find out where people are without either asking or going looking for them. There are some good places to check for RP though. The Feast of Lights, or any other Inn is a good place to start. The Central Square is another place to check. Also, when people are not out RPing or working on skills/forms, they are often in the Ready Room (recall).
My first real suggestion is to RP with everyone you can convince to RP with you. The more people that you know ICly, the more doors that will be open to you. The more people you are acquainted with, the greater the chance that someone will be on that you can RP with. Also, you'll have more of a chance of getting invited to join a guild, or participate in some special RP. In addition, if more people know and like you, there is a greater chance that you will be able to find a teacher.
That is one of the biggest complaints that I have heard from people. "Nobody will teach me forms." I often think to myself, did they look for someone to teach them? These often tend to be the people that don't try to reach out and work for it. There are always a number of people around who are willing to teach forms, skills, etc. even to those who aren't guilded. How do you find them? Just get to know people ICly, as well as OOCly.
Events. It's far from a dirty word, as anyone can tell you. If you hear an Immortal advertise an event, try to get in on it. They usually are special things that you want to be a part of. It's that simple.
Now let's talk about guilds. Wether you come into the game thinking that it's for you, or you would rather not get sucked in...they are good. By good, I don't necessarily mean that it is always good to join them, and you need to toss out thoughts to the contrary. Guilds provide a great way to get interesting RP that you won't find anywhere else, a place to get easy access to skills and forms that it can be difficult to find elsewhere, as well as just good people to talk and RP with. Another thing to consider is that just because you aren't a member of a specific guild, that doesn't mean that you don't have to stay away from them. Most of the guilds are happy to interact with non-guild people, and some are even quite willing to teach them things. Should you decide to join one though, you have a bunch of options, it just depends on what you are looking for. The Children of the Light is the most straight forward combat guild. The Army of the Hawk, and the Borderguard are other good choices for that. There are also noble houses where you can get a good variety of positions. Last but not least of course is the White Tower, where would-be Aes Sedai, and Warders can find their home. Keep in mind that if you are a channeler, you won't be able to join a guild in a combat capacity (for non-random channelers).
A lot of people walk in and think that they need to find the best equipment, which is something of a mistake. There's a lot less need to stress over your equipment right off at tsos than there is at a lot of other places. I suggest finding things that suit the look you're going for rather than just having the best AC. A lot of times, with really good AC will come a high encumberence too. That's a surprisingly important factor in choosing your equipment. The higher that goes, the slower you move, and it can really play a big factor. It's fairly similar with weapons. It's nice to have a good sword, but it won't be that much of a difference early on.
But..what about when you really do need them.. Well there are a few places to look. For weapons, either Zeth, or Krivian Falk is where you want to go. Falk is on the east side of Cairhien, and Zeth is just southeast of recall. For armor..Zeth is a good place to go that's close, but you can find a wider variety off in Amador and some of the other cities.
To get items, you need money, right? It's usually not a huge deal through most of the game, so don't worry too much about it. Getting your hands on some cash can be difficult at first though. Having another player help you out with that can do the trick nicely. Otherwise, you can sell things you find/take off defeated mobs, though that can be tough at first. Frankly, it is going to be hard until you get into level one or so forms, and can start taking on some of the human mobs.
Now, once you have forms and such, what do you do with them? When you are just starting off, stick with animals. And also, stay in Cairhien hunting the little things. Once you are level 1 or so, I suggest the forest area of the Bandit Camp. There are lots of little animals there, Just be sure to stay east of the prickly bushes and you will be safe from the bandits. Find someone to teach you level 2s, and then your options open up a bit. Far Madding has some guards that are worthwhile, and off in Maerone you can find some rogues that are good at this time. This will take you up to level 3.
Some mistakes to avoid:
First off, don't go to the blight until you can handle it. It's a dangerous area, obviously and most people will just die. Similarly, be careful if you are antagonizing someone. That hermit in the robe with the rope belt could be hiding something real dangerous. When you die as a result of RP, it's not a pretty situation. Your character is dead. You'll have to rename, and start over. You do get to keep the same pfile, which means that you'll have most all of your knowledge of forms, skills, weaves, etc...but the Imms will take some off the top. Still.. it's not the end of the world. You don't lose any items when you die, and even if a mob kills you, you just reappear at recall and don't have to go find a corpse.
Other than that, read help files. There's probably too much information there. Also, talk to other players, and don't be afraid of the Staff.