How exactly did Venezuela's economy fail? Venezuela has unfortunately become the example of a first-world, wealthy democracy failing, and I'd like to make sure I understand why.

My understanding comes down to a few major steps, namely:


Venezuela has incredible stores of oil
In the late 90's and early 2000's, Hugo Chavez's government invested heavily in building up the oil sector, and redistributed most of the profits to the people in the form of social programs, and state-owned corporations filling most roles in the economy
The oil industry caused three major strains on private industry in other sectors of Venezuela's economy, causing private industry to begin to fail:


Spike in Venezuela's currency caused by oil exports ("Dutch disease")
Competition from state-owned competitors
Borrowing by the government to reinvest in the oil industry at high leverage

The drop of oil prices in 2007 to 2008 caused a gradual collapse of the one-product economy
Excess printing of money to try to combat the effects of the oil price drop caused hyperinflation and a loss in confidence in the currency
Hugo Chavez and Nicholás Maduro consolidated power in an attempt to more directly target economic issues and administer social programs (assuming good intentions, which may not be a good assumption)
Another drop in oil prices in 2014 caused additional damage to the economy
Protests against the drop in quality of life, and lack of popular support for Nicholás Maduro caused functional collapse of the government, as a government that people don't believe in is no government at all


Where are the holes in the above description, and where do I need to understand better?
I think you summarized most of it quite well. Few things that you missed: 

There was a host of bad macro and microeconomic policies. For example, nationalization of many firms, price controls, subsidizing many uneconomical activities etc. Also actually the investments into oil industry and productivity declined in Venezuela after the industry got nationalized so that part was not fully correct, and Hugo Chavez was appointing people who were making it worse (see  thisforeign policy article).

Also when it comes to social policies, it’s definitely possible and legitimate to want to have Ralwsian welfare state - this is matter of philosophy and value judgements not economics. However, this does not mean that a country can just arbitrarily sets its social policies and ignore resource constraints. Venezuela was running large fiscal deficits even in their best times when oil prices were high save for few years with surpluses.

Moreover, one thing that many states that are running out of money resort to is printing more of them which causes inflation. Now moderate inflation is fine but if you are running large deficits that you can’t really hope to repay with future economic output you need to start printing so much that it will eventually lead to very large inflation which will in turn only accelerate collapse. Once money is worthless people start resorting to barter which is less efficient and just exacerbates the problems further.