Well, much like with regular aircraft, there are four main controls but they are subtly different from how they work in fixed wing aircraft.
Pitch and roll are controlled with the joystick, called cyclic in helicopters. This adjusts the angle of the rotor blades at different sides of the helicopter; for example, to pitch forward, the blades in front will reduce their angle of attack and therefore lift, while the blades on the back will increase angle of attack slightly and cause more lift, so the rotor disk will pitch forward and the fuselage of the helo along with it. Roll works similarly. This control is called cyclic because it causes the rotor blade angle of attack to cycle as the blades go around the rotor disk.
Yaw is controlled by the foot pedals, which adjust the tail rotor to produce more or less sideways force.
Vertical lift is controlled by a handbrake-looking lever called collective. This control adjusts the collective angle of attack (and therefore total lift) of the main rotor assembly. Even though the collective is usually sensible to map to the main throttle axis, it is not the throttle in helicopters and shouldn't be treated as such - it is much more like the elevator in fixed wing aircraft.
The powerplant in helicopters usually drives the main rotor(s) at more or less constant speed. The powerplant can produce certain amount of torque; that sets limits on how much resistance the main rotor blades can be allowed to produce (it must be less than the maximum torque output of the engine - otherwise rotor blades start to slow down or damage the transmission, this is called overtorquing and usually happens with excessive collective angle of attack).
Much like with overusing the elevator in a fixed wing aircraft, using too much collective angle of attack can cause rotor blades to stall, though the stall situations are more complex and there are other ways that the rotor disk can lose lift. Most common anomalous flight states are receding blade stall and vortex ring state, read up on them if you wish.
Basic flight is a little bit different than with fixed-wing aircraft where propeller produces thrust and wings provide lift; in helicopters, the main rotor(s) produce both horizontal and vertical lift, and it is the pilot's job to direct that lift to control the vehicle in horizontal plane as well as vertical axis. It is, in some ways, remarkably similar to flying a lunar lander would be - except much more complex because of the more complicated dynamics, and once a helicopter gets into level flight it actually gains certain characteristics of fixed wing aircraft - for example, turning is pretty much the same: You bank the helicopter to the direction you wish to turn to, then increase collective to prevent loss of altitude, and use the tail rotor pedals to keep the turn coordinated. If you wish to expedite turning, you can also increase pitch attitude.
My experience with helicopter sims is that they require much higher precision and smoothness of controls than fixed wing aircraft. They are also much more challenging because of the hover operations you are required to do to take-off and land them, and much easier to lose control of. Fixed wing aircraft are more stable and I much prefer flying them, but helos are a nice occasional challenge as well.
All in all, though, four axes HOTAS is well enough to control a helicopter. However, helicopters especially benefit from separate rudder pedals because of the sensitivity of the controls - tiny correction of yaw usually results in changes in pitch/roll positions as well with a twist handle stick, and that can lead to it becoming almost impossible to, say, hover.
High frame rates are also almost required for any sort of precision flying such as landing on a helipad or hovering over a specific target.