On a 30 year fixed rate loan, your payment for the mortgage (the principle and interest) will remain the same throughout the 30 years. What happens is that in the first few years, you're mostly paying interest. As the years go by, more of your fixed payment goes to the principle (the amount you actually owe) and less to interest.
For example, on a 30 year fixed rate loan--let's say it's a $100,000 loan and you're paying 5% interest--you'd pay $586.32 a month. In the first year, you'll pay $4,966.49 in interest and $1,475.37 in principle (reducing your mortgage.
In year 10, you'd be making the same $586.32 a month payment, but in year 10 you'll pay $3,887.60 in interest and $2,554.26 in principle
In year 25, you'd be making the same $586.32 a month payment, but in that year you'll pay only $1,305.68 in interest and $5,136.18 in principle.
In year 30, you'd be making the same $586 a month payment, but in that final year you'll pay only $171.13 in interest and $6,270.73 in principle.
However, your actual mortgage payment is usually made up of 4 things: principle, interest, taxes, and insurance. (Sometimes you'll see it shortened to "PITI.") Insurance will probably go up a bit each year. The thing that'll raise your total monthly payments, though, will be the real estate taxes. So your actual payment with those 4 things might start out close to $700 a month, and then gradually rise from there.
There's a very useful mortgage calculator at http://www.mortgagecalculator.org/
You can plug in your own numbers to see what your payments would be.
Hope that helps.