For Manual items, you can simply complete the item by clicking Complete:

The Actions drop down menu allows you to "Complete Item", enter notes, skip item (if no longer relevant), or force complete it (marks item as complete).
​Note: Force Complete is useful for items that were completed outside of your onboarding process (e.g. HR already completed benefits enrollment for the candidate).

Task items in an onboarding checklist act as placeholders for you to create a task that can be assigned. Once the task is created and assigned, you'll see it populate in the contact's activities. Hover over the Task item and click Complete:

eSignature items will launch an eSignature experience for completion.