Crimp Splicing
You start off with a single wire.

Cut it and bare about 8mm from each side.

Take the wire you want to spice in and twist it to one wire.

Push the wires into either side of a straight crimp and use a crimping tool on both ends.

The wires are now all secure, there is no need for heatshrink or electrical tape.
Make sure you use the correct colour straight crimps, red are for thin wires,
blue are for medium wires. Generally, red will be what you will use.
Proper Splicing
Separate the wire you are going to splice into.

Using a sharp blade and a lot of care, strip back the sheathing about 10mm long.

Take the wire that is splicing in and bare the end about 15mm.

Wrap the new wire around the original. You could leave it like this but ideally you should
flux and solder the entire joint. This will increase the contact and stop it pulling out.

To protect the newly formed joint, slide a section of heatshrink tube over it and heat.
If there is no way to get heatshrink over the joint, wrap it in electrical tape.

The completed joint, if soldered and covered in heatshrink, will be perfect.
Less Than Ideal Splicing
As an absolute last resort you could use what they call choc-blocks or cable connector strips.

They are a quick way to splice into cables but I wouldn't use them.
Idiot Splicing
Do not use quick clips, I cannot discourage you enough to steer well clear of these.

Yes they are quick and convenient but the quality of the connection is rubbish.
If you use these, it won't be long until you are ripping it all out and starting again.
You have been warned, don't do it.
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