Before you exit your starter city, make sure to equip (via the Equipment menu) your weapon and Bastokan Ring, along with any other equipment you might have that looks better then what you're wearing. Then talk to the gate guard (in Bastok they're the NPCs with I.M. after their names, or Iron Musketeers) and get Signet. If you're in Bastok Markets you can also talk to Gulldago near the exit (D-11) as well for the tutorial quests which will explain some simple game mechanics.
Once you exit the city, locate the Field Manual and look at Individual Training (or whatever it is called) and select something you think you can do. Don't limit yourself to just killing whatever is on the page you selected because the time spent doing so will probably lose you more experience points then you would net, but try to do some pages to build up tabs so you can buy buffs from the book later. To attack something you merely target and hit attack, then when your TP is at 100 or more you should select Abilities -> Weapon Skills and use a Weapon Skill on a mob (for later reference, when you get the Dual Wield ability from using a subjob of Ninja or Dancer, or you level high enough that you get it natively, always remember to keep the higher damage weapon in your main hand). As a Thief you should also use Steal whenever facing off with Beastman mobs such as Goblins - Silver Beastcoins can occasionally be obtained, which are fairly valuable on the Auction House.
At about level 10 you'll notice that mobs in North or South Gustaberg are Too Weak for you to get experience from in most cases, and you'll want to start heading towards Konschtat Highlands where mobs are tougher, and perhaps even to Gusgen Mines (around L-7 on the map) and put your party flag up for a "Book Burn" there (essentially someone invites you and you grab page 1 in the Grounds Tome and kill skeletons while Level Synced, and you get lots of Experience Points).
Between all this you'll notice that your inventory fills up very fast. Make sure to turn on Auto-Sort in the Config menu if it isn't already, and head back to town when it fills and you're not in a party. When you get to town, either dump your gear with your Moogle in your Mog House, or sell it at the Auction House or to an NPC, but price check via
FFXIAH before just selling to an NPC. If you've had Signet on you'll have crystals, which are quite valuable. If you need Gil to buy better gear and selling your loot isn't enough you can make Copper Ingots using the method I suggested in an earlier post. Remember that Beehive Chips and Honey can sell for a decent amount (although probably not as decent as crystals).
On stats in the game you'll find that your equipment menu lists HP, MP, STR, DEX, VIT, AGI, INT, MND, CHR, as well as Attack, Defense, and elemental resistances. On gear you'll usually find a defense number, and on better pieces listed stat boosts. On weapons you'll usually find Damage, Delay, and occasionally other stats.
HP and MP are pretty obvious if you've ever played any RPG with them before, but for completeness sake HP is the value the enemy has to damage you before you die (and the maximum is the most of it you can have), while MP is used for casting many spells. As a Thief you should have an okay amount of HP and roughly no MP.
For the other stats (and this is not a complete list), STR indirectly boosts your Attack stat and how much damage your melee hits do, DEX increases your accuracy, and crit rate (and boosts the damage ratings of your Sneak Attacks), VIT indirectly boosts your Defense stat, lowers your enemy's crit rate, and plays a minor role in many healing abilities, AGI indirectly increases you evasion rate, parrying rate, shield block rate, and ranged accuracy (and boosts the damage of your Trick Attacks), INT indirectly boosts the magic accuracy and damage Black Magic spells do, indirectly lowers how much Black Magic spells damage you by a small amount (and boosts the effects of certain items like Bloody Bolts), MND indirectly boosts the magic accuracy and damage White Magic spells do, indirectly lowers how much White Magic spells damage you by a small amount, and plays a decent role in how powerful Cure spells are, CHR mostly affects Bard's Song accuracy, and Beastmaster and Dancer abilities, and plays a small role in resisting Bard songs from enemy mobs.
Damage plays a role in how hard you hit mobs, and Delay plays a role in how fast you hit mobs. One useful number to know is the DPS of a weapon, which is [(DMG rating of weapon) x 60] / (Delay of weapon), although you'll have an easier time of just looking at your weapon on the FFXIAH page for it to find the DPS. This is useful for comparing the balance of Damage to Delay on a weapon at a glance.
As you get very high in level you'll find that hitting faster without necessarily having to have a vastly lower damage weapon becomes more of a priority, which will introduce you to the single best stat in FFXI,
Haste. Haste is amazing in that the more you have of it, the better it works, however it has caps (total cap is around 80%), even between sources of Haste. Haste from gear caps around 25%, and the other most common form of Haste, the spell Haste, gives 15% of it. Haste even lowers spell recast times, making it even useful for mages.