There are many versions of amplifiers based on the LM386 chip, described here on Instructables and elsewhere.
I collected inspiration from many of them, and tried to build one that would fit my need.
I would build a simple, portable, battery and plugged in powered guitar amp, loud enough for campfire jams.

Supplies

Speaker, found mine in a recycling bin.
LM386 DIY kit (simplest way to get started, comes with capacitors, resistors, jacks and miscellaneous components), ebay 4$
JFet transistor, I used a MPF102, 1$ (this is a preamp stage since my guitar has passive pickups)
Resistors and capacitors, try the ones you have lying around for the best result you are happy with.
Prototype PCB universal board, 1$
9V Battery
9V Battery connector, 1$

Step 1: Build and Test the Circuit on a Prototyping Board

Since there are so many descriptions of circuits, test your best guess on a prototyping board, connect it and listen to the sound.
Replace capacitors of different sizes to see if you get better results, that you like.
I tested different capacitors together with a potentiometer on the gain-pins to see if I could get some distortion.
I ended up with a 1µF capacitor in series with a 10kΩ potentiometer.
Since there is a 1.35kΩ internal resistor, that would be the perfect size potentiometer, which probably does not exist.
The gain potentiometer only has an effect on the last 13% of its travel, but that is fine.
Cranked all the way up gives a much louder, somewhat distorted sound.

Step 2: Power

Replace the speaker input connector by a metal plate, where you can fit a on/off switch.
I also added a power jack to input 5-12V, which is the voltage span the LM386 op-amp can work with.
My power jack has a cut-off connector I used to disconnect the battery, when a power cord is used.
Be careful of the polarity here, I used positive on the sleeve and negative on the center pin, since that is how my Roland Bass amp is powered.
I put a 100µF capacitor between positive and ground to get rid of noise, but later found that that capacitor should placed as close to the Vcc pin on the LM386 chip as possible, so I added a 1000µF capacitor there as well.
I soldered a 1.45kΩ resistor to a LED and two wires to have a small dim red light from inside the speaker when it is turned on.
I soldered the 9V battery connector and a 9V power connector to the power stage, to be able to easily separate and connect the audio part from the power part.

Step 3: Prepare the Speaker Cabinet for Input Jack and Volume and Gain Potentiometers

Drill holes for potentiometers and jack, where you find they would fit.
The walls of the speaker are normally too thick for mounting potentiometers and jacks, so I removed a bit of material from the inside with a wood chisel.

Step 4: Solder the Circuit

My prototyping board has no connections between the soldering pads, so I had to make all the connections myself.
Since a component layout is quite different from a circuit diagram, I tried to draw and plan for a layout that would require least distance in needed connections.
The result deviated a bit, realizing that some larger components require more space than others.

I connected the positive Vcc power with a wire on the top of the board, and all the ground connections on the back, separating disaster areas by clumsy soldering as much as possible.
The soldering is quite ugly and reflects my skills, but it works fine, which is the most important.

I used the speaker wire to connect the pots and jack to the board, adding a little heat shrink here and there.

I also added a pcb-spacer in each corner to separate the back of the board from the speaker wall.

Step 5: Closing the Enclosure

I fastened the audio board with a piece of patent band, padded with some packaging foam, screwed to the inside wall of the speaker.

I duct-taped the battery to the back wall.

Then I connected the power stage to the audio stage with the internal connector.

Soldered the output speaker wires to the speaker again and screwed it back together.

Connected my guitar, crossed my fingers and turned the amp on.
It still worked, and is quite loud for a little battery powered device.