Program timer

I am working on a project for my son for a water feature. I am to the point it is so big it uses a large amount of water. I am looking into adding a sprinkler valve to control water flow. I am new to coding but I can build any thing. I just ordered an Arduino UNO and a ATTiny85 for final project. This is what I am looking for I would like to have it setup either where you press a button and it will hold power to my relay to allow power to flow to my sprinkler valve for 60 seconds. The other idea I have is that when you push the button water will come on at a random interval between 1 and 10 seconds and remain on for 60 seconds. the button will be a push button when pushed there will be no resistance. any help would be great. thank you all in advance.

Button Examples and Blink Without Delay examples.