Anastasia tours and the other companies too will provide a "blanket visa" that covers your time off the ship while you are with one of their guides/drivers. There is no need to get your own visa unless you want to go off completely on your own for sightseeing. 
Sandy 

This is the information on the
DCL website. You can find it yourself under St. Petersburg, travel information, travel documentation and then click on the link. I was also told that I would need two copies of my passport, one for each morning:
Russian Tourist Visa Sponsorship
Should you wish to obtain an individual Russian Tourist Visa, you will need to be sponsored by a licensed Russian Tour Company. This company will have to create a program and provide a voucher to the Guests confirming all the arrangements along with a reference letter that includes a visa reference number. Once a visa has been issued, it needs to reference the same Russian tour provider as the voucher confirmation. A Russia Tourist Visa will not be accepted by the Russian Immigration official as valid without a confirmation voucher for pre-arranged services.
Guests should consider the following when selecting a tour provider in St. Petersburg. The tour provider:
Needs to be licensed to operate in Russia and authorized to provide services to foreign visitors.
Must be authorized to issue Russian visa reference numbers.
Should be authorized and have a permit to meet the Guest inside the Port of St. Petersburg. If the tour provider is not authorized to enter the port area, you will be advised to meet them at the port entrance, which is located approximately 3 miles from where the ship docks.
The Russian Tourist Visa issued and stamped on your passport will apply only to the referenced tour company, the person named on the visa and for a specific travel date. The sponsor of each tourist visa is legally required to be the provider of services for the Guest named on the visa and will have his or her license revoked if a visa holder is found ashore without a pre-arranged activity.
The above requirements are subject to revision at any time without prior notification. Please also be aware that these regulations can also be at the discretion of the individual officers on duty on the day of arrival and may vary at any time. Additional information is available at the U.S. Department of State website. Visas must be obtained at a Russian embassy or through a visa service prior to departing the U.S. Your passport will be required for issuing the visa.