People who are on a monthly or twice per month payment schedule don't benefit from “extra paychecks”, but anyone who receives their income weekly or every other week means that you actually receive an “extra paycheck” at least two months out of the year.
For most of the year, a weekly paycheck means you get four checks per month. A bi-weekly paycheck means you get two paychecks per month. There are four months of every year (March, June, August and November) that have 5 Friday's instead of four.
When creating your budget, people on the weekly schedule should budget based on four paychecks a month, while people on a bi-weekly schedule should budget for two paychecks a month. In the months when you receive 5 instead of 4 checks, or 3 instead of 2 checks, you should be prepared to use that “extra paycheck” to your advantage. (This only works if you actually have a budget that you stick to, otherwise you'll use the extra money without even realizing you had an extra check).
Many people use their extra paycheck to pay off debts, or boost a savings plan. You might use it towards a vacation, or to buy something you've had your eye on for a long time. Maybe you'll use your extra paychecks to fund your holiday shopping, or as a donation to your church or favorite charity.
Like anything else, in order to make it work you need a plan in place. Start by determining what you spend for your regular monthly bills. Then you can determine how much per paycheck you need to set aside to cover these expenses (and sometimes it's easier to have an account designated for this amount, transfer it automatically each week or whenever payday is for you, and use that account for expenses only).
Figure out how much you pay for irregular bills throughout the year. Things like property or school tax, insurance premiums, Christmas shopping, back to school supplies, car maintenance – anything you pay during the year but not on a monthly basis. Divide the total amount of these expenses by 12 to figure out how much more you need to set aside each month in order to cover those expenses when they come due. It's a good idea to use a savings account or money market with a reasonable interest rate since the money will sit in the account until it comes due and you can let that money earn a little in the meantime.
If you've planned your budget around four pay periods or two pay periods a month, you can then put those “extra” paychecks to work for you however you see fit!