That is right and you all can do it.
First if you get paid every two weeks then this will be a little easier for you. As you are using your budget you will find that you live on a monthly basis. Each month you need the same amount of money but two months out of the year, usually April and October, you receive 3 checks.
From using the budget you will notice that these two checks become extra money and will go into your savings anyways.
What I suggest is to keep your very first 3rd paycheck in your checking account. This will help make using the budget easier because you always have money in your checking account. Another reason is you won't have to worry about paying overdraft fees on your account because there will always be money in your account.
This is also how you can get your emergency fund as well. That money is there and will always be there so if needed for an emergency it will be in your checking account and then can be replenished slowly or when the next 3rd paycheck comes along. It might be that it takes both 3rd paychecks to get to your $1000 goal but you are working toward it and some emergency fund is better then none.
Lets say that you get paid on a weekly, semimonthly, or monthly basis.
For weekly I would suggest that you save every 5th paycheck that you get in a month. It works out to be 4 months out of the year and will equal out to a 1 months worth of extra income.
If you are paid semimonthly (1st and 15th) there are a couple of ways to figure it out. For ease we are going to say that you make $1000 every paycheck.
1. $1000*2 pay periods= $2000 monthly income
$2000/24 pay periods= $83.50 (you divide it by 24 because that is the number of pay periods you have each year)
Total = $83.50 needs to be saved each paycheck
2. This way is if you would like to save as much as someone that was getting paid every two weeks (less being saved)
$1000*2 pay periods= $2000 monthly savings
$2000*12 months= $24,000
$24,000/ 26 pay periods= $923.08 (this is how many pay periods in a year there are for someone who gets paid every two weeks)
$923.08*2 pay periods= $1846.16 ( you multiply it by 2 pay periods because that is how many checks you will save in a year)
$1846.16/ 24 pay periods= $76.92 (24 pay periods is how many pay periods you have in a year)
Total= $76.92 needs to be saved each paycheck
If you are paid monthly I would save a weeks worth of pay on the months that have 5 weeks in them, you can also just save 1/5 of you check, or you can take your monthly income divide it by 12 and you get how much you need to save each month.
I hope that this is helpful to you and that you are able to save a little bit more than you thought was possible by having a budget.