This document will run you through some of the basic differences between Forgotten Realm Characters and Standard D&D characters.
Race
Humans are found in almost every corner of Faerun. They have all the standard traits found in the Players Handbook. The only difference is Humans start out with common and regional tongue for free as languages.
Dwarves are divided into 3 types: Gold, Shield, Gray.
Gold dwarves hail from the Great Rift region. They have all the dwarven traits in the PHB except as follows: +2 Con, -2 Dex; +1 racial bonus to aberrations
Shield dwarves hail from many regions. They have all the same traits as in the PHB.
Gray dwarves (also called Druegar) hail from the Underdark, and are common known as evil. They have many specialties but also have a level adjustment of +2, which means that if your supposed to make a 4th level character that your character will be 2nd level. Talk to your DM if you are still interested in this race.
Elves are divided into five playable subraces: Drow, Moon, Sun, Wild, Wood.
Drow hail from the Underdark and are commonly known as evil. They have many specialties but also have a level adjustment of +2, which means that if your supposed to make a 4th level character that your character will be 2nd level. Talk to your DM if you are still interested in this race.
Moon elves are the most common sort of elves, also sometimes called silver elves, they usually hail from many small elven forest communities. They have all the same traits as the PHB.
Sun Elves hail mainly from Evermeet, the North, Silver Marches, and Western Heartlands. They have all the elven traits except as follows: +2 Int, -2 Con
Wild Elves hail from many of the southern forests and jungles. They are a very feral race. They have all the same traits as the PHB except as follows: +2 Dex, -2 Int; Favored Class: Sorcerer
Wood Elves are reclusive, but not as much as their feral wild elf cousins. They hail from the Dalelands, the Great Dale, the North, Tethyr, and the Western Heartlands. They have all the same traits as the PHB except as follows; +2 Str, +2 Dex, -2 Con, -2 Int, -2 Cha; Favored Class: Ranger.
Gnomes are divided into 2 types: Deep and Rock
Deep Gnomes (also called the Svirfneblin) also hail from he Underdark, and while they are not necessarily evil, they aren't exactly friendly folk either. They have many specialties but also have a level adjustment of +3, which means that if your supposed to make a 4th level character that your character will be 1st level. Talk to your DM if you are still interested in this race.
Rock Gnomes hail from many places throughout Faerun, but never in large quantities. They have all the same traits as the PHB
Half-Elves are the same as the PHB and can be found in many regions throughout Faerun. They can be half-drow, half-sun, half-wood, etc. But they have no special abilities from the intermixing except the half-drow has 60ft darkvision.
Half-Orcs are the same as the PHB and can be found in many places throughout Faerun but are usually found in Amn, Chessenta, Damara, the Moonsea, the North, Vaasa, and Waterdeep.
Halflings are divided into 3 types: Ghostwise, Lightfoot, Strongheart.
Ghostwise are a wild, feral race of halflings that usually don't stray far from the deep forests. They have the same traits as in the PHB except as follows: Speak without Sound (communicate telepathically with one person within 20'); They do not receive +1 racial bonuses to saving throws; Favored Class: Barbarian.
Lightfoot hin are the most common type of halfling in Faerun. They hail from many different regions but are mostly semi-nomadic in nature. They have all the same traits as in the PHB.
Strongheart halflings hail from the region of Luiren. They have all the same traits as the PHB except the following: gain one extra feat at 1st level; they do not receive the racial bonuses to saving throws.
Planetouched are all special races that have many special features about them. They all have a level adjustment of +1, which means that if your supposed to make a 4th level character that your character will be 3rd level. The three basic types of planetouched are Aasimar, Genasi, and Tiefling. Each of them has special abilities for each subrace and the Genasi are even divided into air, earth, water, fire. I'm not going to list every single feature they have but I will list their ability adjustments and preferred Class.
Aasimar carry the blood of celestial being in them and are usually good-aligned. They have +2 Wis, +2 Cha and have the favored class as Paladin.
Genasi a descended from elemental-related creatures. Their preferred class is fighter.
Air Genasi +2 Dex, +2 Int, -2 Wis, -2 Cha
Earth Genasi +2 Str, +2 Con, -2 Wis, -2 Cha
Fire Genasi +2 Int, -2 Cha
Water Genasi +2 Con, -2 Cha
Tiefling carry the blood of evil outsiders and are usually aligned evil. They have +2 Dex, +2 Int, -2 Cha and a preferred class of Rogue.
Class
All Classes are the same as the PHB. There are subtle differences in some classes, but nothing that has to do with stats, just rules, such as Druids receive their spells from a patron deity instead of from nature.
Region
After you have selected a class and race, you then have to choose a Region from where you hail. Regions are important because they give you your regional language, bonus free equipment, and choice of regional feats. The list of Regions is very large, so you can either look that up yourself, or talk to your DM once you've chosen your class/race and he will help you pick your region.
Religion
Players who choose to be Paladins, Rangers, Druids, or god forbid someone actually choose Priest will have to choose a Realms Deity to be a patron of. Just talk to your Dm about that. There are some stipulations on certain religions and others will and won't allow cross-classing with other classes.