The safest and possibly easiest way to power your Pro Trinket is with 3 AAA cells, fed directly into the 5 volt pin on the board. True, it's only 4.5 volts, but that will be sufficient to power it up, and even run a few LEDs.
You don't need power regulator for it?
What do these toys do?
While I cannot point you to a specific tutorial, the most important part of wiring power is to get the polarity correct. Perhaps it is time to purchase a low cost digital multimeter. Using the multimeter, you can (safely) confirm connections and polarities before applying power to a circuit. As you grow with the hobby, a multimeter will become your most basic troubleshooting tool.A $5 cheap-o from Harbor Frieght is perfectly fine for Arduino related work but please don't use the cheap Chinese meters on household voltage, they're not super safe, is especially the probes.
As an side note about polarity, the Trinket has a diode on the VBAT input connection. This prevents any damage to the board if it is connected to reverse polarity since current can only flow one way through a diode, the plumbing analog of a check valve.
But, if you use 3 batteries for a 4.5 volt supply and connect it to the +5V connection, there is no diode. ...
...as the diode causes a small drop in voltage, only about 0.3 volts, but that could represent hours to days of run time with a battery.
LR44: unsuitable, too low in power delivery ability. A CR2032 is about the minimum for a disposable cell.