Right depending on how long you have depends on how much you can see. Moscow is a VERY big city so take very comfy, waterproof shoes that have a good grip, the weather at the minutes keeps shifting from black ice and snow to melting snow and huge black muddy puddles.
I would recomend visiting Red Square, having a walk through GUM and a visit to Lenin is always good. You need to be there between 10am and 1pm and you have to pay 60 roubles to put your camera and mobile into a safe store. Trust me they get very touchy if you try to take your camera into the tomb. Also it's illegal to smile, talk or look happy while in there, my friend and I got told off big time for this by a policeman with a gun.
Just outside of Red Square is Alexandrovsky Sad, a beautiful garden with lots of statues and the monument to the eternal flame.
The Cemetery and monestery at Sportivnaya (south west moscow, Red line) is worth a visit and if free, if you are a fan of Russian Literature, cinema or history then you can see people like Gogol, Bulgakov, Yeltsin etc
Sparrows hill in the south west is home to a beautiful forest and Moscow State Uni (MGU) you can walk around there and the walk is sign posted. It also allows you to have a view of all of moscow and see all 7 of the Stalinist sisters.
If you like animals the Zoo is cheap and full of a huge collection of animals. It's metro station is on the circle line between Belorusskaya and Kievskaya.
For sovenirs go to Izmailovsky park at the weekend, metro stop Partizanskaya. You pay 10r to get in then you can buy everything there from stuffed bears, to t-shirts, to matrushkas and hats, plus if you speak Russian then you can haggle and get a better deal for things. Never pay the price they first say.
If you have time Park Pobedy (victory park) in West Moscow is worth a walk around, and there is a military museum full of tanks, planes, trains and helicopters.
This alone will probably fill up 3 days for anything else use a guide book I recomend 'The Rough Guide to Moscow' everythinf in it is fairly up to date and it's very easy to use.
Right first of all people NEVER smile and always wear dark clothing and basically look depressed, so if you don't want ot stand out look depressed all the time. Ticket wise you can either buy a travel card for 50r then decide if you want a months unlimited, weeks unlimited or whether you want to buy a set number of journeys. This one is good if you plan to return to Moscow at a later date as it can be topped up. Otherwise you can buy a ticket for a set number of journeys eg 1, 2, 5, 10, 20, etc for you as a tourist this is probably better. At every metro station you will have to pay at the Kassa and talk to a very grumpy, scary looking old women, if they shout don't take offence that's just what they do. Also they make ask for more money than your ticket is worth this is usually so they can give you your change as a note rather than in coins.
Eating and drinking
I don't know what your budget is like so it's a bit hard to advise, as a student living here I have found places like Krushka good value, 500ml of beer is 55r, for sushi planet Sushi or Yakatoria, Moo Moo is good for Russian food and it's laid out like a buffet so you can point at things and not really have to speak much Russian. There are literally hundreds of MacDonalds' in Moscow so they are always a good back up and are the best place to pop into if you need the loo rather than pay a 'toilet babushka' to use her portaloo.
For a cup of tea or coffee Kofe-Hauz is good value but watch out for 'hot chocolate' Russian hot chocolate is literally a cup of melted chocolate with a spoon, Kakoa is the closest you will get to hot chocolate but it's very weak and milky. Starbucks on the arbat is the only place so far I have found that serves REAL hot chocolate.
Do not be alarmed at the number of police you will see literally everywhere they only stop and talk to you if you are drunk in public or are up to no good. Usually if you only talk English to them or mention the words 'British Embassy' they tend to go away.
Little old ladies are to watched out for at ALL times, the rule of thumb is the more elderly they look the more visious they are, if you get in their way they will hit you!
The mullet is in fashion and not just for men, you will see some very funky looking fair styles, do not be alarmed most of them do not have a life of their own
Stary dogs- Moscow has 30,000 stray dogs, they are harmless unless you run past them or poke them, if they bite you go straight to the Embassy and get a rabies shot. If will save you from the illness but stop you drinking for 6 months.
A lot of people speak English so if you get very lost or confused try English or German and you may get help.
At the minute the snow has started melting and icicles have started to fall from the roofs and buildings, keep an eye out for them, if a road is cornered off it's probably for this reason.
If you are here around February 23rd it's 'Defenders of the Motherland day' so there will be lots of celebrations going on.
If anyone wants anymore tips for surviving Moscow just message me, I am always willing to help!