Sorry but you sound like you could really use the help of another DJ to show you around the workings of a TT (turntable) in person. But I'll try the best I can in words.
First off there are two basic types of tone arms. There's the s-shaped arm that you see standard on Technics
1200s. And then straight arms that I am almost sure you have on your Vestax deck. The s-shaped arm was designed to angle the cartridge so it would remain parallel to the grooves in the record from start to end of record thus giving beter stereo sound. But with this design came the physics of the force of the spinning grooves pulling the arm towards the center of the record. Anti-skate is an adjustment on TTs with s-shaped arms to counter balance that inward pulling. Straight arms don't need anti-skate. There are fewer forces pulling in funky directions with straight arms so it stays in the groove better when scratching and doing tricks.
Now for some basic TT anatomy:
The cartridge is the entire assembly that you screw on to the end of the tone arm. The needle is the little part that you can remove from the end of it. With the ortofons it's that tiny pyramid shaped thing at the end of the cartridge holding the metal needle. Never pull on the little metal needle itself.
Not sure what the extra weight is because I'm guessing you have one of the Ortofon concorde series that vaguely resembles a banana.
Here's how you set the weight properly assuming you've got the needle in the cartridge and the cartridge screwed on properly to the arm. The next step is calibrating the arm so you know where 0 grams is. Lift the arm out of the rest by the cartridge and let it rest on your finger in that no man's land between the tone arm rest and the TT platter. Turn the weight on the back of the tone arm until the arm lifts off your finger and literally floats by itself, neither dropping towards the platter nor hitting the top of the arm's range of motion. Now turn the small ring on the weight with the little numbers on it, making sure not to move the weight itself, until it lines up with 0. Now the arm is perfectly calibrated for 0 grams.
Look at the instructions that comes with your Ortofon. It'll tell you what the proper weight for your cartridge is, probably about 2 or 3 grams. Turn the entire weight so it comes inwards and stops at the proper weight measurement. The cartridge should come down but don't let the needle touch anything except the vinyl when you're ready to play -- delicate machinery.
Damn! Sometimes the easiest things to do are the hardest things to explain. Hope I didn't confuse you more. Wish I could just throw up a movie file or something.
A couple links that may be of use:
http://music.hyperreal.org/dj/
http://1200s.com/Support/Tech/faq.html
There are tons more if you do a search.
Practice, practice, practice. And don't be afraid to politely ask questions of DJs you see if you are an eager student. Any DJ worth anything won't begrudge you knowledge. The mean, nasty ones probably have complex personal problems that you don't to touch with a 10' lightstick anyway.