Irrigation is normally laid on the soil, under the mulch. Otherwise the mulch absorbs it all and little reaches the plant roots.

As for thickness, as thick as possible without burying the plants and as they grow you add more. At least 4" and 6-8" deep is commonly recommended.

At end of the season that is up to you as it isn't as simple as taking it off or leaving it on. Number of variables - (1) only you will be able to see how much it has decomposed in your climate as the rate of decomp varies greatly, (2) it depends on if you till your gardens or not, (3) if you amend your gardens during the off season, (4) what the weed situation is, etc. So that is a question for the fall.

Dave

Yep, Dave covered it. In the South, mulches can decompose rather quickly. This, although it can periodically require replenishing, is a good thing. Decomposing hay improves soil. You mentioned grass clippings in a previous post, just mix that into your hay every so often and that will help.

You'll have more questions come the end of the season, but whether or not I till in the fall, my beds never go without some sort of mulch. It can be leaves, hay, straw, etc..., or it can be a living mulch - AKA ground cover. As Dave mentions, add this knowledge when fall gets near, you'll have enough to do and learn for now.