According to the general rule, marriages between the Russian and foreign nationals formalized in any other country in compliance with its legislation are deemed valid in the RF. In other words, there is no need to legalize the marriage as such. But you may have to legalize any documents confirming the marriage with the foreigner (Article 158 of the Family Code of the RF; Article 13 of the Law dated 15.11.1997 N 143-ФЗ).
There are two basic methods of document legalization.

Method 1. Simplified legalization (affixing the apostille on documents)
The apostille is applied for using a document in any countries that joined the Hague Convention (The convention that cancelled the requirement for legalization of foreign official documents; it was signed in the Hague on 05.10.1961).

For example, if somebody married a foreigner in Italy (a member state of the Hague Convention), it will be enough for legalization of the marriage in Russia to make sure that the marriage documents bear the apostille of an Italian authority (Articles 3 - 6 of the Convention). After that, the marriage documents will be valid in the territory of Russia.

If you have any documents related to marriage with a foreigner and bearing the apostille, you must have them translated and notarized in the RF (Article 81 of the Fundamentals of the Russian notarial legislation, approved by the Supreme Council of the RF on 11.02.1993 N 4462-1). Any notarized documents related to a marriage that was formalized in any other country can be used in Russia.

Method 2. Consular legalization
If the documents related to marriage to a foreigner have been issued by a country that did not join the Hague Convention, then you need to contact a consular office of Russia located in the territory of the issuing country in order to legalize the documents (Article 27 of the Consular Charter of the RF; Item 10 of the Administrative Regulation of the Ministry of Foreign Affairs of the RF with relation to provision of the state service for consular legalization of documents, approved by the Order of the MOFA of Russia dated 18.06.2012 N 9470).

Please note that consular legalization takes longer than the apostille procedure.
You will need the following for consular legalization (Item 19 of the Regulation):

- an application;
- your passport;
- the document that needs to be legalized;
- a document evidencing that the consular fee and the charge to compensate actual costs.
According to the general rule, the consular fee is USD 30, and the Russian nationals are exempted from any charges to compensate actual costs (Article 36 of the Consular Charter of the RF; Items 30 - 31 of the Regulation).

If the officials are satisfied with the documents submitted, the documents will be registered, and you will get a receipt that the documents have been accepted. The receipt will specify business hours when ready documents can be collected (Items 25, 68 - 70 of the Regulation).
Please come to collect the documents at the specified time. When you produce the receipt, you should be issued:
- either legalized documents, or
- documents without legalization (upon applicant’s request, a written refusal can be issued) (Items 26, 79, 80 of the Regulation).

Please note that the service related to consular legalization of the documents is provided within five business days upon registration of the application for legalization. The period of document issuance must not exceed five days, either (Items 14, 15 of the Regulation). In order to apply for consular legalization, the applicant has to apply in person (Item 19 of the Regulation), so it is unlikely that you would be able to authorize any other person to obtain consular legalization for you.

Useful information on this topic
Official web-site of the Consular Department of the MOFA of Russia - www.kdmid.ru