Help with project

I am new to the use of Arduino uno R3 and I need to know how many things can an arduino operate? Can an arduino uno R3 run multiple programs?

Well it only runs one program at a time, but it can do many things sequentially, over and over. The loop() function in every Arduino sketch runs "forever", and so each time through the loop you could for example check a bunch of sensors and act according to what you find- eg activate solenoids and move servos.

Thanks man, so it can run multiple items and say when this sensor is tripped open this one, when this other sensor is tripped open number 2 and so forth?

Arduino Uno (Atmega328) can run hundreds of solenoid valves by using shift registers.
You can also use them to sense hundreds of simple on/off sensors and even analogue ones by using multiplexers.
Exactly how many depends on how fast you need to operate the valves and how often you need to check the sensors. The more you have the more time it will take.
A microcontroler can only do one thing at a time, but it can do simple stuff in rapid succession and give appearance that more things happen at once. It's just that your program needs to be written in an adequate form.

Cool thanks man, I just need to now learn how to write the code for the arduino.

Well, start with the Learning section.
Bliink without delay is very handy for running things concurrently.
State machines will be handy for what you describe also.

Thanks man I have been reading a lot and have gotten better at programming but I still need help with it.