The arcpy polyline geometry object has a very helpful method called
positionAlongLine (value, {use_percentage}). This function finds either a distance (in the feature's coordinate system) or the percentage from the line's starting location. It then returns a PointGeometry object that can be used for further analysis, or that can be saved out as a feature class using the CopyFeatures tool. If you use the optional use_percentages, false means it's a distance, true means it is a percentage with values between 1-100. If a value is great than the length or over 100 % then the last point is used. If values are less than 0 or less than 0% then the first point is used as well.
Assuming you have a line feature class, just create a search cursor and begin accessing your locations.
fc = r"c:\temp\lines.shp"
with da.SearchCursor(fc, ["SHAPE@"] as cursor:
for row in cursor:
print row[0].positionAlongLine(10, True)
print row[0].positionAlongLine(10, False)
Enjoy
