Are the breadboards the thick white plastic ones with the square holes? (Please show us a picture of your breadboard) If so, then you can use plug your parts directly into the holes and use #22 solid wire to connect them. There are long conducting strips that run the length of the breadboard, usually 2 on top and 2 on bottom. Then there are vertical strips of 5 contacts each. The voltage used depends on the supply voltage needed by the parts. Many parts use 5 volts.
The voltage and current stated on the back is what it is maximally rated for. But 300 volt is certainly not save to apply to it. Or for the components that you insert the leads of into it. Even 9 volts is too much for many common parts. Please do show the details of your powersupply too. Did you mean a basic 9 volt battery block? Or some sort of wall-wart adapter? It sounds like you’ll be better of if you stick this following product into your board, and supply it with 9 volts from the adapter. But maybe the plug won’t fit. It does supply a regulated 3.3 volt and 5 volt which most parts rely on to be supplied with.
Get yourself some solid wire as Dave mentioned. Basically the metal core should fit into the holes with some pressure. (but not so much that it bends) Stranded wire is no good for these. You’ll never keep the strands together when you insert it. They’ll just bent and fan out like a tassel. And ‘tinning’ them together with solder is not going to work either. It’s too irregular in thickness. Of course you can cut and strip whatever length of solid wires by hand as you see fit. But I like how orderly my breadboard look when I use a box of these. A breadboard full of ‘spaghetti wires’ is so confusing. It induces mistakes.
Usually the holes in the lanes on the side are connected through along the length of it. Use these for the positive and negative voltage rail. (often there is a printed plus and minus on it) I have one that has a break midway (needs jumper wires) and is twice as long as yours. Each string of 5 holes (maybe 6) going out from the center line are connected in-line together. Stick the legs of components that need to be connected together in those. Stick the other legs of a component in adjacent rows of 5 holes (or a bit further depending on the part size and circuit complexity). Each row of 5 is not connected to the neighboring string of 5 holes on either side of them. Also, they do not connect to the other side of the center line.
It’s best to measure the connectivity between holes with a resistance meter (multimeter). If you want to figure out where the metal goes. It may be a bit of a (small) investment for a prime beginner. But it is an essential tool to learn how electricity flows. And how much voltage or current is at play. Some are dirt cheap and good enough as long as you don’t stick it in a wall-powersocket, or appliances connected to it.
While you can try and poke the legs of a led with 1000 ohm resistor in it, with 2 additional probe leads in various places, to see when it lights up. You risk putting wires in the wrong places and create a short circuit. Then things tend to get warm and start to smell. Beware of that tell tale sign that something is wrong! You won’t get electrocuted with 9 volts. But parts may get broken with that voltage applied to it.
But this sparkfun breadboard tutorial probably does a better job at explaining how it works: