Q:

How does one create petroleum/crude oil for future generations?

I am a geological novice so maybe this is a wrong question. But the idea is to create a thought experiment. How does one "create" petroleum or crude oil for future generations? Is it enough to bury a lot of trees underneath the earth at great depths and eventually thousands (maybe hundreds of thousands years) later crude oil is formed? 

A:

Geological processes are just too slow. Although, given how quickly we are pumping greenhouse gases into the atmosphere, humanity may well (in a generation or two) be growing biological material as fast as possible and throwing it into deep holes in the ground, which will give another fossil-fuel resource in a few million years. But we'll be doing that just to sequester carbon dioxide from out of the atmosphere, not to invest in future hydrocarbon supplies.
Hydrocarbons are useful because they have very high energy density: the energy stored per unit weight and unit volume is extremely high. Furthermore, that energy can be harnessed with very primitive technology - just burn it. Because we've been relying on them for nearly two centuries now, we've got very good at safely transporting them globally, and safely storing them in a form ready for immediate use.
So, hydrocarbons have two uses: one, they act as storage, as a time-buffer for time-sensitive energy demands such as electricity consumption. And two, their energy density makes them very suitable for powering transport on irregular or changeable routes.
However, as a means of energy storage, they're not very efficient: even the best CCGT gas-powered electricity generators are only 60% efficient; and internal combustion engines tend to give an efficiency of about 20-25%, tank-to-wheel. And that's without the losses involved in creating the hydrocarbons in the first place
So whether hydrocarbons have a future as a source of energy is very dubious, because for almost all applications, we now have superior options.
And the future for fossil hydrocarbons must, for the sake of human civilisation, be short and quickly-tapering, because of the risk of catastrophic global warming.
For some transport applications, the energy density is still a winning attribute of hydrocarbons: most notably, powered flight for freight and travel.
We already have two routes to non-fossil hydrocarbons: biological sources, and direct chemical synthesis. Each involves capturing atmospheric CO2, and combining with water, to generate a blend of hydrocarbons.
Now, we already have means of creating hydrocarbons suitable for flight (e.g. Jet-A and Jet-A1 fuels). And there are already demonstration plants that have closed-loop generation of synthetic hydrocarbons, for use in electricity-grid-balancing, by using surplus electricity to synthesise methane, which is then burnt in gas turbines when required. Similarly, Tony Marmont's team have been synthesising petrol (gasoline) from air, water, and electricity.
However, none of those things mean that hydrocarbons necessarily have much of a future, beyond plastics production. Because hydrocarbon-powered aviation has a lot of environmental problems beyond just CO2 emissions, in particular it makes other contributions to exacerbating global warming. And there are lots of options for energy storage within the electricity supply chain.

A:

This isn't really a complete answer, more of a footnote to @EnergyNumbers answer.
(Aside: I'm not sure what the definition of a 'geological process' is, but it's not quite fair to say they are 'too slow'. Leaving aside a philosophical point about scale invariance, it's easy to think of fast geological processes. So maybe we can't reject the hypothesis on the basis of time alone.)
Lots of (especially shallow) gas is biogeneic in origin, as opposed to thermogenic. Indeed, Rice (1993) estimated that biogenic gas accounts for about 20% of natural gas resources. Depending on the organic content of the sediment and on the electrochemical environment, methane begins to be produced by various micro-organisms as soon as burial commences, especially in low-oxygen environments. There is tons of literature on this, look for 'organic matter diagenesis' and people like Charles Curtis.
Here's the reaction:
$$\ce{2CH2O + H2O -> H+ + HCO3^- + CH4}$$
In other words, organic matter plus water (and bugs) results in bicarbonate (which may end up as a carbonate cement) and methane. 
Why is this not a real answer? Because 'methane' is not 'petroleum' and certainly not 'crude oil'. Biogenic gas tends to be 'dry' (mostly methane), which makes it rather less valuable (i.e. energy-dense) than thermogenic gas. 
Reference
Rice, D. D., 1993, Biogenic gas: controls, habitats, and resource potential, in D. G. Howell, ed., The Future of Energy Gases - U.S. Geological Survey Professional Paper 1570, Washington, United States Government Printing Office, p. 583-606.

