> how to power the heater filaments.
They are just like light bulbs. Feed the rated voltage and they do their job.
You can plug-in a desk lamp, right? You could probably wire-up a lamp from a plug, socket, and some wire. Or wire a car tail-light bulb to either a 12VDC battery or a 12VAC transformer. Same deal.
Big difference is that most heaters can work red-hot instead of white-hot like a lamp. So they last forever, pretty near.
It is simpler than you think.
Complications:
There are 7, 8, or 9 pins down there, be sure you get the right ones.
AC heat causes hum. A thin direct-heat filament cathode will get hot/cool twice per cycle, humming-up the signal. Separate heater-cathode tubes can be heated with AC and give very low hum, because the separate cathode holds the heat over a 50/60Hz wave. Hum in indirect heat tubes is mostly about those AC wires near your grid and plate signals. Keeping the AC balanced and well away from signal pins can give excellent results.
You need the "right" voltage. Most general-purpose tubes use 6.3V, a relic of using lead storage batteries as heater supply. We call these "6V", and in RMA type-numbers these usually start with "6" (6SN7, 6L6, etc). The nominal voltage is really 6.3V, but 10% or even 20% variation makes very little difference. And in some situations, under-volting the heater works better for small-signal use.
But design for nearly any voltage is possible, and lots of tubes were made for 12V, 25V, 35V, 50V, 60V, and even some 117V heaters (for direct operation from a US wall outlet). You often find the "same" tube in several heater voltages: 6SN7 and 12SN7 are the same except for heater needs. (But 35L6 has nothing to do with 6L6!)
Some tubes like 12AX7 are dual-voltage. They have two heaters, brought out on three pins. Typically: parallel both heaters and feed 6V, or series the heaters and feed 12V. This comes naturally when you have a twin-triode (two heaters) on a 9-pin base, and it avoids having to stock two versions of the "same" tube for different uses. Be sure you wire right. Putting 12V on a 6V series connection will light-up white-hot and die in hours. Putting 6V on a 12V series connection won't get hot enuff to boil any electrons, won't work.
Oh: Welcome to the Lab!