It seems that two processes are required to establish a successful
- Dialing in and locking the addresses with the correlating chevrons
- Creating a stable wormhole from the source gate to the destination gate
This answer attempts to explain the 2nd requirement, since the 1st
is relatively easy.
Typical Stargates: Ground Based
For typical, ground based stargates within the Milky Way gate system, as well as the Pegauses and (Universe)/Destiny/Seedship system, power is supplied by the DHD's Cold Fusion Reactor Core1, which also powers the DHD itself. While not explained directly in cannon, power is likely transferred from the DHD's power source wirelessly2 through either microwave radiation, or more likely induction, since both the DHD and the stargate are made of the superconductive Naquahdah3.
Typical Stargates: "Space Gates"
Gates that are fixed within the vacuum of space (space gates), most typically found in the Pegauses gate system, possess attached power nodes4, which are affixed along the outer edge of gate. While the method of power is not exactly known, most likely the power source of each node is a modified version of the Cold Fusion Reactor Core, with the addition of electrical RCS stabilizers.
For atypical cases, in which a DHD is absent or damaged, power can come from a number of sources, though in some cases those sources may have undesirable behaviors:
- Static Electricity via lightning (SG-1, Torment of Tantalus)
- Current Electricity via heavy-gauge conduit (Stargate @ Stargate Command (SG-1)); via jumper cable (SG-1, 1969)
- High Energy Electromagnetic Radiation via energy weapons fire (Atlantis, First Strike)
- Extreme Gravitational Fields via black hole (SG-1, A Matter of Time)
static and current electricity, high energy electromagnetic radiation (e.g., microwave, infrared (heat), x-ray and gamma-ray), and even indirectly from strong gravitational fields.