Interesting that you have concluded that this is a "VERY" simple implementation considering your self confessed exposure of only 5 minutes to the arduino environment.
avgod - don't take bainesbunch's reply as .. harsh.
He's got a point, yeah, the problem is generally simple, but it requires some non trivial knowledge on figuring out what those papers actually say and where from to source nowadays a ttl to 232 level adjuster. Yeah max232 but you can't just plug in an IC in, it needs a PCB or some wires or passives soldered in..
So a suggestion for both, can you find/produce the remote control (IR codes) to remote-control it from arduino instead of wiring it? (it is also more flexible from positioning/placement of the arduino circuitry POV)
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PS E,G, there is no "D0Rx and D0Tx" in either papers you provided nor arduino nomenclature. So yeah, your message may seem crystal clear to you, but it has a certain level of cryptography included you are not aware of being non-trivial to decode it.
The software part is indeed VERY simple. A 10-minute or so job, including debouncing of the buttons. Press button, react with a Serial.print() command.
The hardware may be harder to do, unless you have all those pieces in place already.