As the pool captain you can approve a player's membership to your pool in your pool's Management section.
1) Open the relevant tournament
2) Hover your mouse pointer over the Pools tab
3) Click on the cog icon to the right of your pool's name to open the pool management area
4) Click on the Applicants button on the left (you should see a notice in red informing you of how many pending applicants you have)
5) Click on the Approve button next to the relevant player's name.