Working with PICmicros is not that difficult, as they are designed to work in several ways of power supply and source of clock.
Beginning by the power supply, PICs can be powered by batteries or by power supplies (linear or switched mode). The most common voltage is 5V, but it can vary from 2 to 5.5V (depending on the model of PIC). Using voltages around 4 to 5V is error proof, as it can be available by three 1.5V cells in series. I think it is the more simple way to supply the PIC. Variations can be obtained with 9V or 12V batteries and a linear regulator IC (for example the 7805 or 78L05 for 5V output). Different and variable voltages can be possible with the LM317 regulator IC with adjustable voltage output. Supplying with the mains power network need a transformer (110V to 8Vac) a rectifier and some reservoir/filter capacitors, and the regulators ICs described before.
This will save the batteries.
No matter what the way you are supplying power to the PIC, you should connect a 100nF bypass (ceramic) capacitor near the 2 rail pins (the Vdd and Vss) to filter against noise, glitches, coming from or generated by the whole circuit.
Some words about the oscillator (source of clock):
PICs can be clocked by external sources (oscillator circuit), or with the addition of some components (quartz crystal, ceramic resonator, or resistor-capacitor) compose the oscillator built in some pins.
The easier and more simple way is to use the internal RC oscillator, that does not need any additional component. The disadvantage in the accuracy and stability. If you need accuracy, go for the crystal based oscillator (and two more 22pF capacitors).
The oscillator type is selected by the fuses configuration, and depend also on the frequency. The lower the operation frequency, the less power the PIC will consume.
All these details are available in the datasheets.