Basically, unless you have contacts within Russia, go to one of the Visa specialists. They know what can be done, how it is done, will organise the necessary Invitation from a Russian organisation, and handle the Application for you. For a fee of course - but it is a fairly competitive marketplace.
To get an idea of what's involved look at the Russian Embassy
Russian Consulate and their handling agent
Russia Visa
The increasing difficulties over the last few years are a direct result of deteriorating relationships between the two governments and diplomatic 'tit for tat'.
One fairly new obstacle is a year multi entry visas no longer mean a year but have a restriction of 90 days in 180, giving the whole thing a 360 day lifespan.
A 'tit for tat' example - last year the British Embassy in Moscow stopped accepting personal Visa Applications and said they must be channelled through a handling agent - who charge a fee! In response, the Russian Embassy in London has now done the same - adding £25 to the already high cost for 5 day (actually a full week!) service or £32 for next day service.
And when protesting to your MP for a change in relationships and mutual easing of the Visa regieme, point out that the Russian Embassy charges a £30 fee for (for example) a 1 year multi-entry business visa, next day service to EU citizens. Unless that EU citizen also happens to be a UK citizen, when the Embassy fee for the same work/document increases 10 fold to £300 - plus the £32 for their Handling agents!
Rant over.