For example, which of these is correct:
Ich esse gern Pizza
Ich esse Pizza gern
It depends. When you want to express that pizza is your favourite meal you can say:
Ich esse gern Pizza.
When you admit that you would be happy to eat pizza, e.g. that has already been ordered or served, you would say:
Ich esse Pizza gern.
In the first case, I would prefer "gerne" instead of "gern".
The "proper position" depends of emphasis:
1) Ich esse gerne Pizza means I like pizza. (As opposed to hamburgers or frankfurters.)
2) Ich esse Pizza gern means "I like pizza." (As opposed to hate it.)
In either case, the part to be emphasized is at the end of the sentence.
Between the above, 1) is considered a bit more "standard" than 2)