Speculation alert: This is not documented anywhere in any of the films or TV series. Books, fan fiction, and other media may cover this, but I am unaware of their explanations. Here are some of my theories:

Because a T1000 is made up of billions or trillions of nano-machines, and each nano-machine has a 'return to essence' capability, it can be concluded that each nano-machine caries its own power supply.

This can be done several ways:

1. The nano-machine can be a catalyst, which facilitates chemical reactions of elements commonly found in the atmosphere without itself becoming altered. These chemical reactions could release tiny amounts of energy which could be captured by the T1000 in much the same way tiny photvoltaic cells contribute to the whole of a solar panel.

2. Each nano-machine contains a tiny amount of radioactive material, perhaps only a few atoms worth, which can produce energy which is captures in the same way as mentioned above. Tactically, this would be a poor design, as anyone capable of detecting radiation would pick up on the signature.
   There are elements with short half lives, Radon 222 for example has a half life of just shy of 4 days. This could ensure that the decay does not happen too slowly to be useless as a power supply, but not so fast that the power supply burns itself out prematurely.

3. I am going to steal @Aaron Digulla idea of the pre-charged capacitors for this one, because that also seems like a viable idea in the event a small part of the T1000 becomes separated from the whole. (he gets an up vote from me because of his originality)

Speculation alert: This is not documented anywhere in any of the films or TV series. Books, fan fiction, and other media may cover this, but I am unaware of their explanations. Here are some of my theories:

Because a T1000 is made up of billions or trillions of nano-machines, and each nano-machine has a 'return to essence' capability, it can be concluded that each nano-machine caries its own power supply.

This can be done several ways:

1. The nano-machine can be a catalyst, which facilitates chemical reactions of elements commonly found in the atmosphere without itself becoming altered. Platinum and Palladium do this in a cars catalytic converter. Upon capture of reactants, the nano-machine becomes slightly heavier than the nano-machines which have no reactants, and are drawn below the surface exposing reactant deficient nano-machines to the atmosphere. Once inside the reactants could be brought together to begin a reaction. These chemical reactions could release tiny amounts of energy which could be captured by the T1000 in much the same way tiny photvoltaic cells contribute to the whole of a solar panel.

2. Each nano-machine contains a tiny amount of radioactive material, perhaps only a few atoms worth, which can produce energy which is captures in the same way as mentioned above. Tactically, this would be a poor design, as anyone capable of detecting radiation would pick up on the signature.
   There are elements with short half lives, Radon 222 for example has a half life of just shy of 4 days. This could ensure that the decay does not happen too slowly to be useless as a power supply, but not so fast that the power supply burns itself out prematurely. Radioactive decay has been used to power several satellites and probes that mankind has sent into the cosmos, and knowledge of this technology could have survived the nuclear war.

3. I am going to steal @Aaron Digulla idea of the pre-charged capacitors for this one, because that also seems like a viable idea in the event a small part of the T1000 becomes separated from the whole. (he gets an up vote from me because of his originality)

I am not a big supporter of the radio wave resonance theory, since after the war, it's likely that many radio towers would have been destroyed by nuclear weapons, or rendered useless by the EMPs produced, and therefore unavailable in great supply during the war with the machines.

Solar power seems an unlikely candidate because in the post nuclear war world, there could still be fall out clouds in the atmosphere, and then there is the challenge of keeping a charge going during nighttime operations.