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Compass and Straightedge Constructions with videos:  http://www.regentsprep.org/Regents/math/geometry/GC1/indexGC1.htm

 

Basic Constructions: http://constructions.homestead.com/

 

Triangle centers:

 

Orthocenter - Altitudes ( vertex perpendicular to opposite side)

Circumcenter - Perpendicular bisectors of sides - a circle with the circumcenter as its center will circumscribe the triangle

Incenter - Angle bisectors - a circle with the incenter as its center will be inscribed in the circle

Centroid - Medians (vertex to midpoint of opposite side)

The Euler Line -  orthocenter, centroid, circumcenter, (also incenter when isosceles)

 

 

http://www.mathopenref.com/triangleincircle.html