For example, visit the Tretiakov gallery. If you are even not the great admirer of art, it will impress you. So, if you are a student it will cost very cheap - 10 rubles (with presentation of your student's ID card, not obligatory Moscow ID card), and if you are a foreigner you will have to pay rather a big sum of 150-200 rubles. Try to find Russian friends, who will buy a ticket for 10 rubles for you. Be ready for your legs ache. It's not so easy to walk around 70 halls. But, if not stay too long by each masterpiece it's quite possible to see everything for an hour and a half.
It is reasonable to devote the second day to the beauties of Moscow. The Cathedral of Christ of the Savior. This majestic construction is to be seen. This cathedral is advised for obligatory visiting by all travel guides. On founding yourself inside the cathedral, you will feel pride for Russia. Visit the Red Square and the Kremlin. Probably, there is no such person who would not dream to visit these places. Buy the ticket for students, walk around the whole Kremlin, all ancient cathedrals and churches. The Kremlin is not simply the Red Square, it is the whole complex. If it is be possible visit the Museum of Armor.
If you are going to stay in Moscow for only 3 days visit one of the most interesting places there on the third day - the Moscow zoo. Strangely enough, but some people are mostly impressed by the zoo. You will see such quaint animals, birds and fishes which you can see neither in Cologne, nor in Berlin zoos. Have you ever seen a bird with a crown on its head and with a red tie on a neck? You will see it there. Not to be lost in the zoo, you may buy a travel guide.
For the picture to be full, simply take a walk on the streets of Moscow: Tverskaya, Jamskaya, on Novyi and Staryi Arbat. Feel an atmosphere of the city, the rhythm of its life.