There are tutorial NPC's in the starter cities. One should approach you the first time you try to leave the city, or you can seek them out directly. Here is a link to the cyclopedia page about them:

https://ffxiclopedia.fandom.com/wiki/Tutorial_NPC

The basics are pretty simple and you'll get a handle on it fairly quickly.

The normal line of progression for a new player is this:

1. Start leveling. You probably want to start doing this within the first few minutes of being online. Depending on what job you chose you will be provided with either a weapon or spells; a belt if you chose monk. You can begin leveling immediately outside whichever starter city you chose. One thing to keep in mind when leveling solo at early levels is that you can "Check" the mob you're about to fight by targeting it and selecting the "Check" option in your pop-up menu. At these early levels you'll want to stick to "Easy Prey" through "Decent Challenges". The battle mechanics are fairly simple and you should get a handle on them after a couple of fights.

2. As you kill mobs you will accrue items. Some items are worth gil, others are not. Familiarize yourself with the Auction House system and how to buy/sell items. For those just starting out here is a good guide to making gil in the early levels: viewtopic.php?f=6&t=756

There are some NPCs that have shops set up around town that will sell you armor/weapons. Particularly at lower levels it is cheaper to buy from NPCs than it is from the Auction house, but this ratio won't last very long.

The Auction House itself is just where other players will place items for sell and other players will bid on them.

3. After playing solo until about level 12, you will want to make your way to Valkurm Dunes. Here you will either get invites to or form your own party. In a party you will begin to perform the task which your job specializes in. If you've chosen a melee job, odds are you will just be attacking and doing weapon skills. If you are a mage, you will stand back and not engage with the mob, but rather cast spells through the duration.

4. At Level 18 you will need to get your "Sub-Job". Having your subjob is critical and don't expect yourself to level much further than level 18 without it. The standard quest that most people do to obtain their sub job can be found in Selbina located in the Valkurm Dunes. Depending on what mobs you fight in the dunes you may already possess the items required to complete it. If not, many players are helpful and someone will eventually help you obtain these items. We've all been there, we've all done it.

At this point you're pretty much left up to your own devices. You will learn through chatter these general landscape of things and what you need to do to plan your own path in order to be successful.

Some things to keep in mind:

A. Find a Linkshell. Linkshells are basically groups of people in their own private chat rooms. Shouting and asking for one will usually net you a pearl (devices that allows you to communicate with the linkshell). Or usually someone will offer you one if they notice you don't have one. These communities will be the people you end up playing with most. They will help you, but you should also help them. You will learn a lot of things from these people.

B. Also, the above linked FFXIclopedia is an invaluable resource and pretty much contains knowledge of all things FFXI. Keep in mind though that Nasomi is an '05 era server so some information found in the encyclopedia might not be accurate.

Enjoy the game! There's lots to do!