Without passing comment on the posts above about the difficulty in finding the hotel from Osaka Umeda station, here is the easiest and most foolproof way I can think of to describe this.

1) Make sure you are somewhere in the Osaka Umeda JR West (West Japan Railway Company). The JR bit is important, there are 7 stations in the complex, but the main JR station is well signed from all of them.
2) Once you are in the JR Station, follow the signs for Hotel Granvia - this is on the south side, fully built into the station building, and is extremely well signposted in Japanese and English.
3) At the entry area to the hotel you will see the main South Central Exit door to the outside. Go through it, outdoors and to the roadside You will see Hilton East Plaza on the right. Cross the road and you are there.

A lot of the confusion comes from the use of the underground passageway system but the above - staying on the station's main floor level - just makes it as simple as possible. Also there are some references to the central exit, this is perhaps slightly misleading (ok, totally incorrect). A photo of the door is below, which was taken by the station entrance for the Granvia. If you could see through all the concrete blocks on the right side of the photo, the Hilton would be right there. It is actually quite simple, it's just there are almost no signs to the Hilton within the station complex.

There is a temporary issue that there are roadworks going on, so you can't directly walk from the door below to the road, you have to walk around it a bit, but if you leave this door with a view to getting to the roadside then with a bit of weaving around you will get to the Hilton. Also there is a taxi / road entry to the Granvia, which is not signposted in the station, but if you got to that, you would see the Hilton behind you anyway.