What are the 2 types of enzyme inhibition and how do they work?

The 2 types are: Competitive and Non-competitive.
Competitive inhibitors work by mimicking the shape of the substrate, they are specific to the shape of the active site of the enzyme and will take the place of the substrate, in the active site. This prevents the real substrate from interacting with the enzyme and carrying out the usual process, causing inhibition.
Non-competitive inhibitors will attach to somewhere other than the active site, on the enzyme. It will cause changes in the primary, secondary and tertiary structure of the enzyme complex and therefore alter the shape of the active site of the enzyme. The substrate that would usually be specific and complementary to the active site of the enzyme would no longer be able to bind and the usual process would not be carried out, causing inhibition.