Not quite like a telephone
Being a little more complicated than a telephone, although similar in principle in terms of "dialing", the stargate must dial for an outgoing wormhole
and an incoming one. When the stargate dials, as you will doubtlessly know, the centre ring with the chevrons spins so that each of seven chevrons is rotated to the top of the gate. Each time a chevron in the address gets to the top, one of the wedge-like locks opens and closes, whereupon the nice red light glows on, indicating that that chevron has been locked. When all seven chevrons are locked, the wormhole is opened.
I mention this probably rather obvious fact in order to support my next statement: when a wormhole is established, it is necessary for both gates to be "in phase" as it were -- unlike a telephone which can simply accept any incoming call, the stargate uses the slightly more complex principles of quantum physics, meaning that
both gates must dial, maybe in order that some kind of hyperdimensional resonance is set up between them to establish the wormhole. I would imagine that, rather than the wormhole "going out" from one gate and connecting to another, it would need to be mutually established between both gates simultaneously. Perhaps it's just me, but that seems to make a lot of sense.
There's another reason that both gates should dial. If I were to dial Abydos, I would have a wormhole established to that planet. However, if someone from Chulak also tried to dial Abydos, it isn't as simple as just getting a "busy signal". If the gates did not both need to dial, I could theoretically cause some rather severe problems by linking a wormhole to a gate that was already open. Technically, it could probably be done; ie, you would have two wormholes leading to one gate, rather like a 3-way phone system, however it's easy to forget how much power is required. Probably, a gate would be unable to support the extreme power drain exerted by a dual-wormhole system.
With regard to the series then, as far as I remember, the only time a gate has not dialed when there is an incoming wormhole was when it was
already set to the coordinates of the dialling gate. That is to say, if I go to Chulak using the Earth gate, and no one uses the Earth gate again, when I dial back from Chulak the Earth gate will still be "connected", and will not need to redial. That being said, there have been numerous occasions when speed is of the essence and we see Carter, O'Neill or whoever smash in the coordinates for Earth on the DHD when they just
came from Earth and no one has used the gate since...as the coordinates are still set, all they should need to do is hit the nice red button on the DHD. Of course, this
could be explained: perhaps O'Neill wasn't sure if you
could simply hit the red button again so, rather than
try, he wasted all that time redialling the address
With regard to these time-is-of-the-essence situations, we often hear the gate make noises, but never get a shot of it spinning. A reason? Oh yes -- that gate can only manage a certain rotational speed, and the noises are happening a lot faster than I reckon it could actually go. I suppose this, too, could be defended; perhaps the gate actually
can spin really quickly, and uses its excellent intuitive feature to determine how fast it should rotate based on the speed at which the chevrons are entered on the DHD...