These molecules are very similar in shape to the substrate of the enzyme.
They compete with the substrate for the active site of the enzyme.
They fit into the active site and block it off from the substrate.
This prevents a sustrate from entering and forming an enzyme-substrate complex.
Less product is formed per unit time.
To overcome this issue:
You can increase the amount of substrate. This makes the substrate more likely to bind with the active site as it will now be the more effective competetor.
Here is a simple diagram
These inhibitors do not fit precisely into the active site so bind somewhere else on the enzyme.
This distorts the enzyme and the active site changes shape.
The substrate is now no longer complementary so can not fit into the active site.
No enzyme-substrate complex can form.
To overcome this:
You would add more enzyme to increase the concentration of enzyme. Adding more sustrate will not help the situation because the non-competitive inhibitors will still bind to the enzyme as there is nothing stopping it.
Here is a simple diagram of non-competitive inhibition where the red bit is the inhibitor