Frankincense and myrrh are both resins -- dried tree sap -- that come from trees of the genus Boswellia (frankincense) and Commiphora (myrhh) common to Somalia. The way that people collect the sap is similar to the way people collect rubber tree sap or pine tree sap. Cutting the tree's bark causes the sap to ooze out of the cut. The sap used to create both frankincense and myrrh comes slowly and is allowed to dry on the tree. The hardened sap is collected and used as frankincense and myrrh.
Both in the time of the three wise men and today, frankincense and myrrh are most commonly used to create incense. You mix frankincense with things like spices, seeds, roots, etc. to create different aromas. Traditionally you burn the powdered incense with charcoal in a censer or on a small stand.
Frankincense and myrrh are extremely common today and you can buy them from places like this.
Here are several helpful links: