I did the trip DME to this Holiday Inn and back on the train - no big deal and pretty easy. I was towing my rollaboard and backpack which I had to carry up and down some occasional stairs in the stations, but, I didn't really find it that inconvenient.
As others have noted, you'll want to count off stations and pattern match the signs.
When you get off the AeroExpress and intothe Metro station, look for the windows with a mob in front of them and a sign that says Kacci. When you get to the window hold up ten fingers (for a ten ride pass) and given them some cash - I think it's like 250 RUB.
Ride the #5 circle train 3 stops counter clockwise and then switch to the #1 train and ride it 2 stops to Sokolniki. When you get out the hotel will be behind you with a bunch of flags and stuff in front of it and rod iron gates.
The colors of the signs in the stations aren't really indicative of the line colors on the maps. There are numbers for the lines which match the numbers on the map though. The way I found the right trains was to look at the signs overhead on the platforms and find the first few Cyrillic characters matching the last station in the direction I wanted to go in.
There is a map in nearly all the stations I used before you go through the turnstiles somewhere on the wall with a You Are Here arrow. Never saw such a map on the platforms though.
Here is the map:
http://engl.mosmetro.ru/flash/scheme01.html