Visas to Russia can be issued by the Consulate Department of the Russian Embassy in any country (except Russia).
If you need to receive Russian business visa you have to submit to the Consulate Department an Invitation letter from a Russian company.
Such Invitations are processed through the Ministry of Foreign Affairs of the Russian Federation and is required for a single entry, double entry and multiply visa.
Depending on visa duration you can get your Invitation by fax or by courier mail (courier mail is for extra charge).

Once your application form has been submitted to the Ministry, no fee can be refunded after Invitation has been processed.

According to the law of the Russian Federation it is strictly required that visa should be registered by within 3 business days after arrival.

If you have a single or double-entry visa, you could register it in our office free of charge if you are going to stay in Moscow no longer than 3 weeks.
Other visas have to be registered in UVIR, the central official agency that registers foreigners in Russia.
Registration in UVIR takes 5 business days and should be done by the organization which issued your Invitation.
Registration means registering the address where you live in Russia. If it is a private flat, you must get notarized letter from your landlord.
If you move to another apartment, you must register again. This will take another 5 days.
If you don't register your visa, you can be fined while leaving Russia or even departed from the country.
The cost will be 30$.

You can stay in Russia for unlimited period of time.
If you have the correct visa type, you can stay for example 4 months, go out and come back the same day, and stay for another 8 months.
But don't forget that if you stay in Russia for more than 183 days at one time, you are liable to pay tax.

Multiple visas cannot be extended.
Other types of visas can be extended from 10 days to a month.
That will depend on the type of visa, your citizenship and other factors.
If it isn't possible to extend your visa, you will have to get a new Invitation and then a new visa.
In that case you will have to obtain a new visa in a consulate of Russian Federation outside Russia.
The cost will be from 20 to 30$.