For starters, well done, it looks like you have most of the parts you need there, a multi jamma cart like that is a great place to start too, hours of fun.
I see you are going for a Jamma style wiring system. Great. However you seem to have a LCD/TFT monitor. But with your multi game, you have VGA out, so you're OK. Just know that if you were to buy a REAL Jamma game, the wiring is designed to take signal to a classic monitor. So in future you may either want to get hold of an old monitor , or go for a converter card like this.
http://www.ebay.com/itm/NEW-Arcade-game-RGB-CGA-EGA-YUV-to-VGA-HD-video-converter-board-HD9800-GBS8200-/170860805754?pt=LH_DefaultDomain_0&hash=item27c818fe7aHowever that said, looks like you have done your reseatch, and you can take the game to the screen. All you need is a VGA cable , basic PC one to take the picture out of the cart to the monitor.
Power. Study this, there's really no shortcuts here.
http://www.thesupergun.com/wp-content/uploads/2011/02/jamma_pinout.pngSpeakers, OK you have two, so that's more complex, commonly jamma just has 2 wires and you can wire in either way, but if you want to hook up two the power needs to be OK.
Check this out, you might want to hook up one to start and move on.
http://www.hometoys.com/htinews/jun05/articles/nigelb/fig2.gifFor the wires themselves, study the jamma diagram, label every wire, check check and check again.
Hope this helps.
You need to get power to the power supply. Just buy a long kettle lead and chop off the end, trim the wires and connect up the AC and ground. This is a UK image, but follow the black plug and you get the idea
http://img.photobucket.com/albums/v325/Francoberasi/Wiring%20sales/WiredPSU.jpgButtons, you need to understand how buttons work, I learned by watching a delusional video on daisy chaining, sometimes he comes to this forum, but it made the penny drop with me.
here..
https://www.youtube.com/watch?v=FABmvlXON44&list=UUAByuBPBL-WY1AhS0WNnANA