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Teaching Burd the ropes

You can now choose which quest you wish to do next; After speaking to
martin you know you need to get the armor of Tiber Septim, however
speaking to Jauffre he asks you to close a gate that's just opened outside
of Bruma. You can choose to either close the gate, or to ask Jauffre about
Talos to find out where to find the armor.

I chose the first, so let's handle the Bruma gate first shall we. Jauffre
sends you to find captain Burd, who's standing just next to the Oblivion
gate. The catch here is, you shouldn't simply close the gate for them, you
should show Burd how it's done.

So travel together with Burd and two of his guards through the gate and
into oblivion. Once there be prepared for some heavy resistance, but don't
worry as you came prepared. Again at the very center you'll find the
Tower that contains the sigil stone, so follow the path untill you wind up
north of the tower, then travel south to find the entrance. The entrance is
facing west.

Just like at the kvatch tower, fight your way upwarts. It should be easier
due to the help of Burd and his men. Beware though in the rending halls,
there are some nasty spikes coming out of the walls here, and even a
falling blade. Make sure to avoid them.

Above that is corridor of dark salvation and above that your goal, this
towers Sigillum Sanctus. Kill the daedra there, and have Burd next to you
as you touch the Sigil stone to shut down this gate and be brought back to
just outside of Bruma.

Report back to Jauffre and you'll have finished the quest.