For legal reasons, sweepstakes often need to be open to people who aren't members of your program. There are two ways to get those entries in.
Open the sweepstakes in the admin (Rewards › Sweepstakes) and scroll to the Manual Entries card. Click + Add Manual Entry and fill in:
First Name and Last Name — both required
Entries — how many entries to give them
Email — optional
Phone — optional
Click Queue Manual Entry. The entry is queued for processing, so give it a moment rather than submitting twice.
Everything you've added shows in the Manual Entries table with the name, email, quantity and phone. Manual entries take part in the winner draw just like member entries do.

For a stack of paper forms, use an import instead. Go to Reports & Imports › Imports in the admin, start a new upload and choose Manual Sweepstakes Entries.
Here is a sample file.
Your CSV needs these columns:
contest_id — the sweepstakes to enter them into
first_name — the entrant's given name
last_name — the entrant's family name
entries — how many entries to give them
And one optional column:
email — the entrant's email address, when you have it
So a row reading 9999, John, Doe, 1 creates "John Doe" with one entry in sweepstakes 9999.