How much does it cost to enter the park?

Its free, but there is a parking fee in some places

It was a 5 dollar fee to park at the 100 giants trail

Sequoia National Forest is free there is some at cost to you campsites, as for the Sequoia National Park does have an entrance and camping fee.

Just need to have a National Park Pass. 1-7 Day pass is $30. Year pass is $80.