The settlers acquired Indian lands through the doctrine of discovery (simply locating land and laying claim to it), transfer from the English crown, and treaties with the Indians.
Treaties are documents between two independent sovereignties to negotiate borders, provide access to resources, and settle land and military disputes.
The colonists settled mostly on the east coast because the English government had forbidden encroachment of the colonists west of the Appalachians. This policy was intended to maintain peace with the Indian tribes and discourage any alliance between them and France.