I would speak to your employer and ask him if he minds you taking a 10 minute break at a certain time for your prayers. Let him know that if he needs you to clock in and out for this break, you are willing to, and that if he needs you to work over 10 minutes then you are also willing. Also let him know that you are not asking for other personal breaks, as others do, such as smoke breaks. You are only asking for a short time for prayer.
In America, employers are not supposed to discriminate on the basis of religion. Obviously, this does not mean that they never do. What it does mean is that if your boss refuses to allow you to take a break for prayer off the clock, but other employees are permitted to take smoke breaks on the clock (as is often the case) then you can have a case. Unfortunately, employers who are not happy with things of that nature will look for others reasons to fire someone, so if your employer is not happy about it then you will have to watch your back and be upstanding in your job (as an individual should be anyhow).
How many prayer times occur during the work day? One? Two? If speaking to your employer and requesting a few minutes personal time does not work, then I think the Vale's Lily had some good suggestions about praying on your lunch break or requesting a bathroom break. Also, if you are given the time for prayer, don't take advantage of it and return late every day or be caught doing things other than prayer. It is important for employees to be good stewards of their employer's time.