According to Kevin Drum at Mother Jones, here are the "five main drivers of the 80s boom [i]n order of importance":

1. Paul Volcker easing up on interest rates/monetary aggregates in 1982

2. The steep drop in oil prices after 1981

3. Reagan's devaluation of the dollar

4. Reagan's deficit spending

5. Reagan's tax cuts

Drum goes on to claim that his list debunks the conservative "fairy tale":

Conservatives will never admit any of this, but there's no reason the rest of us have to go along with their fairy tale about Reaganomics. Taxes matter, but they simply don't matter nearly as much as they claim, and it's long past time for the mainstream press to acknowledge all this. It's hardly controversial anywhere outside the Fox News bubble.

In his earlier work on the same topic from 2011, Drum expounds on the oil price impact:

If you're looking for other reasons that the 1980s were boom years, No. 2 would be oil prices. The American economy is highly sensitive to oil prices, and after peaking at around $100 per barrel during the Iranian revolution (in inflation adjusted terms), oil prices steadily dropped, falling below $30 in 1986 (again, in inflation adjusted terms). This was largely due to (a) reduced demand thanks to the recession; (b) reduced demand thanks to CAFE standards and other conservation/efficiency improvements that followed the oil shocks of the '70s; (c) increased oil supply from Prudhoe Bay, which peaked in the early '80s; and (d) increased oil supply thanks to a Jimmy Carter executive order ending price controls on oil. Again, Ronald Reagan had very little to do with it.

It is true that the inflation-adjusted average price of oil dropped from $105.81 in 1981 to $31.17 in 1986, and down to $29.86 in 1988 – all in constant 2014 dollars.

But by 1988, the U.S. was consuming more oil than it was in 1980.  That doesn't square with Drum's narrative.  If reduced demand supposedly caused oil prices to plummet, then what happens to this argument when we bring up the fact that demand actually increased 7.6% between 1981 and 1988 while the real price of oil declined 68%?

And about that increased supply: the U.S. was producing 4.0% less total oil (crude oil, tight oil, oil sands, and natural gas liquids) in 1988 than it was in 1980, and field production of crude was down 5.3% during Reagan's terms.  Prudhoe Bay had a negligible impact on overall U.S. crude production, since the 1980s peak (which occurred in 1985) was only 4.3% (or about 400,000 barrels/day) higher than it was in 1980.  This relatively small short-term increase in production, especially in a global context of more than 57 million barrels/day being produced at the time, cannot explain the large drop in oil prices during the entire decade.

The largest decline in oil prices came after the end of the 1981-82 recession, so clearly that cannot be a determinative factor for the oil price decline.

While low oil prices encourage U.S. economic growth – on that, the historical data since WWII is clear – during Reagan's presidency, there was a lot going on in terms of economic policy that diminished the usual role of oil prices.  This is evident in Reagan's economic growth data on a year-by-year basis.  The two highest years for growth during his terms were 1983 and 1984.  There is simply no relationship between oil prices and growth from 1983 through 1988.

The other problematic causation Drum attributes to the Reagan boom was exports: "And there was the Plaza Accord of 1985, which devalued the dollar and helped spur exports. That was also Reagan's doing, but again, it's not something his admirers say much about today, since modern tea party orthodoxy insists that this amounts to 'debasing' the dollar."

Between 1980 and 1986, the inflation-adjusted value of U.S. total exports actually declined by 14%.  By 1987, the decline relative to 1980 was still at 7%.  Again, the most rapid growth under Reagan occurred during 1983 and 1985, and from 1980 to 1985, the real value of American exports declined almost 20%.  By the time Reagan left office, exports made up a significantly smaller percentage of the U.S. economy than when he started, and the decline in their role was most dramatic during the periods of highest economic growth.

This doesn't support the argument that Reagan's economic miracle was driven in large part by increased exports from a devalued dollar.

On the other hand, Reagan's tax reforms did have a major impact, as a series of analyses by the Tax Foundation clearly show.  While it is difficult to disentangle the relative importance of all the causes behind Reagan's economic progress, it's likely that tax reforms are higher up the list than oil prices or the dollar's devaluation.