I wanted to add some helpful references. The 6th edition of the Gilbert Developmental Biology textbook is available on NCBI bookshelf. It's a bit old (2000), but much of the information is still relevant. You can search this textbook for specific terms but not browse.
There is also a collaborative science/fashion project between the Storey sisters, called Primitive Streak, which documents the early stages of human development.
For any given developmental process, there are a number of genes being activated and/or inactivated at that stage that determine how and when structures grow. Events can determine axes too; for instance, the dorsal/ventral axis of the embryo is determine by how the embryo blastocyst implants in the uterine wall. The left-right axis of the body is determined by the direction that fluid travels through a structure called the node, which is directed by hair-like structures called cilia. If nodal flow is backwards, your internal organs will switch sides, called situs inversus.
Back to the limb example... in tetrapods, or animals with 4 limbs, the area where limbs emerge is based on Hox gene expression, and whether or not it will become a forelimb (arms) or hindlimb (legs) is determined by either Tbx5 or Tbx4 gene expression, respectively.
The proximal-distal axis (proximal = towards the trunk; distal = away from the trunk) is determined by FGF gene expression, which induces formation of a structure called the apical ectodermal ridge (AER).
The anterior-posterior axis (head to tail) is determined by Sonic hedgehog gene expression in a region called the zone of polarizing activity (ZPA).
The dorsal-ventral axis (back-front; or back of the hand/arm - palm/inside of arm) is determined by the Wnt7a gene being expressed on the dorsal side.
The outgrowth of the limb is determined by Hox gene expression.
Digit (finger) formation is dependent on cell death between the fingers - hands start webbed, kind of like ducks, and then genes such as the BMPs cause cells between the fingers to die.
Terms to look up for more detail, since I don't have enough street cred here to post more than 2 links yet:
- Snapshot Summary: The Tetrapod Limb (Gilbert book)
- apical ectodermal ridge (AER)
- zone of polarizing activity (ZPA)
- situs inversus
- Hox genes