Included in the kit is a 25' spool of 22AWG black hook-up wire and a pair of wire strippers. To hook up electronic components on a solderless breadboard, you need to have various lengths of breadboarding/"jumper" wires to connect them with. To start, cut 10 3" pieces and 10 6" pieces of wire from your spool. Next, use your wire strippers as shown in the video to strip off 1/4" of insulation from each end of each piece of wire:

Congradulations! Now you have a set of jumper wires to use with your solderless breadboard. If you need more jumper wires, just follow this guide again to create whatever quantity of jumper wires you need.
Jumper wires make prototyping rapid, but can quickly lead to messy breadboards if you have lots of components in a small space. For short runs, I favour this method:

Strip twice as much insulation from the end of a length of wire than you need to make a connection.

Line the wire up against the breadboard holes, with the boundary between the insulated and uninsulated parts of the wire directly above the hole you wish to insert the wire into. Snip the wire directly above the other hole using a pair of side cutters.

Slide the insulation along the wire, taking care not to bend it.

Bend the ends of the wires at right angles (like a staple) and insert into the board.

This method may take more effort, but has certain advantages - you end up with short wire links that fit neatly into the breadboard, and the bend in the wire is not near the point that you stripped the insulation so it's less likely to snap off inside the board if you nicked the wire core by accident. Eventually you should end up with a collection of wires of varying lengths, so assembling circuits can end up a bit like trying to find an elusive Lego piece.

For longer runs, jumper wires are the easiest choice; using a mixture of the two styles of wiring should give you the advantages of both.
Good tutorial (with lots of pictures) on making short jumper wires Ben Smile

I never really liked using the really short jumper wires for things other than connecting to power, ground, and sensitive parts where a longer wire would attenuate the signal too much though; sure they're easier to navigate and maintain signal quality a little better, but they're a major pain to pull out and reinsert into the breadboard over and over again :/
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