How many radio frequencies would you typically use on a sector ?
A sector will involve the use of many frequencies. It will start by listening to the ATIS, then clearance delivery, ground, tower, departures, control....and then from that point we'll have a frequency change about every half hour until nearing the destination, when ATIS, radar, arrivals, tower, ground, will be the rough sequence. A company frequency will also be in use for about the first and last 50 miles. HF is being used less and less, as data links take over...but they aren't everywhere yet, and they don't always work.
Is each frequency programmed in prior to take off so that when required all you need to do is press a button ?
No, you have to select it via a keypad or dial system. The radio control panel (RMP) in the 380 uses a keypad, and the one system controls all of the comms (3 VHF, 2HF, transponder, satcom). There are three RMPs (Capt, FO, spare)...so any box can control any system.
All of the radios have an active frequency, and a spare. When we are given a frequency change, we change it on the spare, and then swap it with the active. That way, if we make a mistake, and end up talking to thin air, a quick swap back will put us back onto the original frequency. If you listen out to other people's calls, you'll hear the frequencies they are sent to, and can normally have the spare already set up before you actually get a change.
Over the years, as frequencies have become more congested, the use of smaller spacing has become more prevalent. Thirty years ago, the frequencies always consisted of 4 digits (i.e. 120.5). Slowly but surely though, five digits crept in (125.75), and now, in Europe we're often hearing that last digit being used (128.755). Radio calls that consist of something like a 'turn right heading 125, climb to FL250, and call Fred on 118.755' tend to run me out of numerical memory at about the ninth digit. The first digit of the frequency is always a '1' (on a VHF system, UHF - military might be a 2 or 3), and the sixth digit is always a '0' or '5'.
The frequencies used are discussed here:
Airband - Wikipedia, the free encyclopedia
How many frequencies are the same in different parts of the world ?
All of the frequencies would be used many times by agencies in different parts of the world. About the only standard ones are 121.5 and 123.45. The first is the international emergency frequency, which most people have selected on at all times. The second is a chatter frequency, which is used so that any quick conversation between aircraft happens off the in use ATC or emergency frequency.