First of all you need to issue a foreign passport by contacting the department of registration of foreign passports of the Federal Migration Service of Russia at your place of residence. All the necessary information (the list of documents, the rules for filling out the application form, the deadline for execution, etc.) is on the official website of the Office of the Federal Migration Service in Moscow.

For a trip to Greece, in addition to having a passport, you must obtain a visa. If you make out a trip through a travel agency, then simply contact the company you like, make your wishes, choose a hotel. All that is required of you is a list of documents that the travel agent will voice.

If you are going to visit Greece yourself, then you need to issue a visa yourself. The Visa to Greece page details what needs to be done and what documents are needed for this.