Not hard (chemically) at all. Air contains water (H2 and O2) and CO2 (carbon.) With those you can make any hydrocarbon. You start with electrolysis of water into H2 and O2. You combine the H2 and CO2 via the Sabatier reaction to produce methane and water. You can use the methane as-is (natural gas) or you can use the reverse water gas reaction to produce carbon monoxide and hydrogen, a mix called syngas. Syngas can then be used (via the Fischer- Tropsch process) to make longer chain paraffins and olefins, which are liquids and can be used as fuel.I was HIGHLY skeptical when I saw this one but after reading the article I'm in the "maybe" its legit camp.
It is also INCREDIBLY energy intensive, and that energy would generally be better used elsewhere.