I suggest two kinds of savings accounts

One for accumulating cash to pay those annual, and semi-annual bills or bills that span over two or more pay periods. Taxes, Insurance, bi-monthly utilities, etc. And if you get paid twice a month, weekly or biweekly you could use this account to gather the funds to pay your monthly bills. This is a relatively short term account. This could even be a interest bearing checking account to make things easier.

The second savings account is for actual savings. Long term savings. You'll set a certain amount aside each pay day for this one. 5%, 10%, of your net or gross pay. Or maybe a dollar amount.

Getting back to our short term account, let's say you get paid every two weeks. Now take any bill that spans more than one pay period. A monthly bill, a bi-monthly bill or a yearly bill.

For a monthly bill you need to multiply by twelve. Since you get paid every two weeks you'll then divide this amount by 26 (there's 26 pay periods in a year). This is the amount you'll need to set aside every payday to cover this bill (if you're current on the bill when you start).

For a bi-monthly bill you need to multiply by six. Since you get paid every two weeks you'll then again divide this amount by 26 for the 26 pay periods in a year. This is the amount you'll need to set aside every payday to cover this bill.

A semi-annual bill would be multiplied by two and for a annual bill you'd then just take the actual amount and divide by 26. As these bills come due you should have enough in this account to pay them right from these funds.

If you were instead paid weekly you'd use 52 to divide by and if twice a month you'd instead use 24 to divide by.

Continue this process until you've figured up all your bills. total up the "payday amounts" and on the next payday take that amount and start a second checking or savings account. Now pay whatever bills you'd have paid anyway until the money runs out. If you run out of cash before all the bills are paid you'll need to dig into your pocket and pay those from there or else call the creditor and explain why you can't pay them. You wouldn't have been able to pay them anyway so there's no difference at this point.

In practice you'll be slightly short for a time. But some bills will help you through the initial shortfalls. Let's say the next bill is paid every other month divide again by 26 to get the amount per payday. This is what should help you make up the shortfall until the savings takes over.