Obviously as a clandestine guerrilla group IRA finances and weapon-smuggling are shrouded in a veil of secrecy, so any figures are by their nature incomplete.

For an official source, there is the intelligence report "Northern Ireland: Future Terrorist Trends", prepared in 1978 by the British Brigadier-General (later Sir) James Glover. (Rather embarrassingly, the report was captured by the IRA in the mail and later published in their newspaper Republican News).

In Tim Pat Coogans book "The Troubles" (1997) the part of this report which dealt with IRA finances is briefly summarized. Firstly, it must be understood that the IRA needed money not merely to buy weapons, but for prisoner welfare and support of dependent families, propaganda work including funding their aforementioned newspaper and IRA volunteer wages. Glover estimates this expenditure in 1978 to be around £780'000.

As to where the IRA got their money, there were several sources. Organised crime was obviously a major money maker. IRA units would fund-raise by robbing banks, post-offices and security vans. (There was even a large art heist in 1974.) These activities went on both north and south of the Irish border, and continued past the Good Friday Agreement of 1998 into the present day. (It's probably outside of the scope of your question, but the IRA was blamed by both the British and Irish governments for the Northern Bank Robbery in 2004, where a gang netted over £26 million.)

There was a spate of kidnappings in the 1970s and 1980s: businessmen such as Thomas Niedermayer, Don Tidey, Ben Dunne and Tiede Herrema were all held for ransom.

In addition the IRA engaged in fraud (welfare fraud, piracy, counterfeit goods), cigarette smuggling and fuel laundering. According to Martin Dillon's "The Dirty War" (1991) the IRA would extort businesses for protection payments, with the city of Belfast divvied up between Republican and Loyalist armed factions.

It was not only organised criminal activity that provided funds either. There was the income from raffles, bingo and dances held under the auspices of the republican movement; there was donations to the prisoners welfare fund (the Green Cross) and money from legitimate businesses like the Black Taxi service (which is still going on in Belfast to this day).

Glover reckoned that the IRA netted £950'000 from these activities: with the £780'000 subtracted that left £170'000 to buy arms with. (I'm pretty sure these figures are underestimations though, as they would certainly have gained more in robberies in different years.)

Quick note on the weapons: in their final act of decommissioning, in 2005, the IRA got rid of-

• 1,000 rifles • 2 tonnes of Semtex • 20-30 heavy machine guns • 7 Surface-to-air missiles (unused) • 7 flame throwers • 1,200 detonators • 11 rocket-propelled grenade launchers • 90 hand guns • 100+ grenades

(Source "Jane's Intelligence Review")

This doesn't account for arms that may have been lost over time or arms that were forgotten about. Some weapons may have been stolen from IRA arms dumps by dissident republicans unhappy at the IRA ceasefire (such as the Real IRA which was formed in 1997.)

These weapons came from a variety of sources: Irish-American sympathizers in the US (through NORAID) supplied a huge amount of weaponry, including the infamous Armalite rifles. Weapons were bought from continental arms dealers, and allegedly from groups like ETA and the PLO.

The main source of weapons, though, was Colonel Gaddafi of Libya. He supplied the IRA with hundreds of tonnes of weaponry, primarily in the 1980s. It should be noted that the IRA didn't have to pay for these weapons: Gaddafi was apparently happy to offer them if they were to be used against Margaret Thatcher's government, as the British had supported the US bombing of Tripoli in 1986. In the event about 1/3 of the Libyan weaponry was intercepted and never reached the IRA. The remaining 2/3's, however, completely re-equipped the the organisation; the Semtex in particular proving particularly vital to the prosecution of the armed campaign.

Sources:

"The Troubles"- Tim Pat Coogan (Random House 1997) -"The Dirty War"- Martin Dillon (Arrow, 1991) -"A Secret History of the IRA"- Ed Moloney (Norton 2002)