When I was in college I had a very simple savings plan. I used cash for all my spending (easier then than now) and when I would get change I would throw it in a bag. Usually by the end of the year I would have around $75.
When I started working and using plastics (credit\debit cards) to make purchases instead of cash, I had to make some changes. First let me preface this, if you have credit card balances or student loan balances, focus more on getting those paid off first before worrying about major savings. Once you get up to about one paycheck worth of savings then focus on the debt before you build it up much more.
The basic plan I recommend for starting off is easy. Keep your checking account with an even amount of money. Depending on your comfort levels you can set this to be an even $5 at the lowest up to an even $100. I recommend starting at $10 since the math is easy. So every time a transaction hits your checking account move an amount into savings that will make the checking balance divisible by ten. You may want to set a minimum balance for your checking of about a weeks expenses so you always have fast money to cover. This may not be as necessary if your savings is in the same bank as checking and can do an instant transfer. For example you pay your credit card and now have a balance of $736.42, move $6.42 into savings so your new balance is $730.
As your income grows and you are able to budget better. You may want to change to setting a maximum value for your checking account to around three weeks of typical spending. When you get paid whatever is over the maximum amount move to savings. Be sure to remember in both scenarios, if you have a big expense that requires you to dip into savings, move that money over and don't pay overdraft fees! For example if you set your max balance to $1,500 and after getting paid you have $1,732.46 then move $236.46 into savings to keep your max balance at $1,500.
There are lots of different savings strategies to do, some are better than this one, but I think it's an easy one to get started. The most important thing is to have a plan. I hope this helps and feel free to leave comments about savings strategies that have worked for you!