How do I get my base to produce better food and oil?

I am assuming that you have trained a lot of troops and you are now running out of resources. There are ways to increase production but unless you are willing to reduce your troops then you will generally always struggle with these two resources. It is better to concentrate on earning as many resource box rewards from daily events, clash of zones events etc. You wont run out of the resource and as you level up the minimum value that you will stick at will raise.

To increase production though, make sure you upgrade everything, Change class to farmer if you aren't already. Look for heroes that you can station in farms and oil refineries. The purple hero Oil Tycoon (for example) has very useful skills to increase fuel production.