Layaway is paying something off in increments while the store holds the item in reserve for you until you've paid in full.
There is almost always a limit to the length of time a store will hold a layaway item while you pay. This is usually 90 days.
There is sometimes a fee charged for using layaway. Sometimes this is a flat fee, like $10 or $20, other times this might be a percentage of the purchase price, like 5% or something.
Payments are not scheduled or in any particular set amount. Basically you pay what you can when you can. There is however usually a minimum down payment when you begin the layaway. This is up to the store and can vary a great deal.
You can usually cancel the layaway at any time and get your money back, but often a store will charge a restocking fee if you do.
If you exceed the time limit of the layaway terms, there is usually a fee charged. For example, if it takes you more than 90 days to pay off and take possession of the item, a store may charge a fee, say 10%, to extend the terms.
This is usually the process for guns and non-guns alike, the sole difference being that with a gun you fill out a 4473. You don't fill that out however until you make your final payment and take possession.
Also, different places might do things just a little differently. Pawn shops for example don't usually charge a fee to use layaway. Retail stores usually do.
If using layaway, make sure you understand the terms before putting an item on layaway, and make sure you adhere to them. Otherwise the item you purchased could end up costing you more than you intended to pay for it.