Invite link
Under Community → Invite you generate a link. Whoever opens it joins directly (or requests to join, if you require approval).
The link doesn't expire on its own, and you can generate another at any time — the old one keeps working until you disable it.
Approval-gated entry
Under Settings → General you turn on "require approval". From then on, clicking the link creates a request, not a member.
Requests show under Members → Requests, one of the four fixed menu items. You approve or decline one by one, or all at once.
Approval is a good filter for a niche community and a bad one for a large one: if people wait days, they cool off. If you're not going to check daily, open entry is better.
When someone pays
Purchase cleared = access granted, instantly, without approval. It makes sense: whoever paid was approved by the payment itself.