Short answer: pick a cost, type the password, run. Verification works the other way round: paste the stored hash and the password, and the page compares them.
Why bcrypt, and why the cost matters
bcrypt is deliberately slow, and the cost factor sets how slow. That slowness is the defence: an attacker with a GPU can test billions of fast hashes per second, but only a few thousand bcrypt guesses. Raising the cost by one doubles the work for everyone, including you.
The 72-byte rule
Input past 72 bytes is ignored. A 100-character passphrase and its first 72 characters hash identically — the page reports it rather than pretending the whole string was hashed. If you need longer input, pre-hash it (for example SHA-256 then base64) before bcrypt, and be aware that changes the format other systems expect.
Generating a password to hash? Therandom string generator makes one locally.