Notary law is entirely state-based in the US, so exact requirements, fees you're allowed to charge, and application processes vary, this is general orientation, not a substitute for checking your specific state's Secretary of State (or equivalent) notary handbook.
Most states require: an application to the Secretary of State (or county clerk in a few states), a background check, sometimes a short training course or exam, a surety bond (protects the public, not you), and a notary stamp/seal purchased once commissioned. Total cost to get commissioned is usually a few hundred dollars including the bond.
Being a commissioned notary lets you notarize documents. Becoming a Notary Signing Agent, additional certification (commonly through the NNA) plus a background screening most title companies require, is what opens access to loan-signing work, which pays significantly more per appointment than simple document notarizations.
Nearly every state caps the fee you can charge for the notarial act itself, often in the $5-$15 per signature/stamp range. This cap does not apply to a separately disclosed travel or service fee, which is standard practice and is where most of a mobile notary's income actually comes from. See the notary fee calculator to separate the two cleanly on a quote.
A surety bond protects your clients if you make an error, it does not protect you. Separate E&O insurance is worth carrying, especially once doing loan signings where mistakes can have real financial consequences for a home purchase or refinance.