Simply clean the area around the joint with steel wool and squeeze the compound onto the joint area. It's that simple. However, make sure you are working from the inside. The finished job looks much neater that way. Hangaer straps are simply a strip of aluminum molded around the outside of the gutter.
Most breaks are due to the failure of the rivets that hold the strap together.
This is easily repaired by substituting a screw for the defective rivet. If the gutter itself is bent or damaged, then try to straighten it while it is in place. If this can not be accomplished then you need to remove that section of gutter and replace it. In this case simply score the sealant at each end of the section with a knife , remove the hanger straps and securing nails. Everything starts small.