Cleaning my new semi auto shot gun????

[D.L.M.]

Hey i have a Q about cleaning a shotgun for anyone whos knows some stuff about it.
i have a new semi auto trap gun and am not sure if im cleaning the barrel right.

am i supposed to run the brush through a [censored] of times with solvent on it, and then run dry patches throught till they come out clean

or am i supposed to use the brush, then some patches
then the brush again, then some more patches etc...

i ususally use the lattler method and it takes forever to get the patches to come out clean. but that may be that stickin the brush back into the barrel gets it dirty again.

whats the deal here?????/
thanks