A Presidential Pardon does not affect the States at all
A president clearly can not pardon himself for a state crime, because the president does not have that as an enumerated power. Presidential pardons are limited in the Constitution, Article II Section 2 Clause 1.
The President... shall have Power to grant Reprieves and Pardons for Offenses against the United States, except in Cases of Impeachment.
A person convicted of a state crime is not convicted of an offense against the United States, and thus, the conviction does not become moot by a presidential pardon. He stays incarcerated, as he is still convicted in the state prison and not pardoned of the state crime.
It takes a pardon from the state's governor to pardon a crime on the state level.
Ohwilleke's excellent answer covers the problem of a person being president trying to pardon themselves of a federal crime.