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Mainframes do not have "buttons" on the screen. Mainframes use PF keys to do similar functions -- but the way they work is completely different than a PC environment; unlike a PC nothing on the mainframe screen is transferred to the computer until the appropriate key (clear, enter, PF or PA key, etc) is hit.
IBM has a number of documents about using web interfaces with CICS -- even CICS legacy applications. I recommend you go to the IBM web site, search for CICS and web and start reading the documentation. This will take some time but it will be time well spent.