You need to start with either a friend or an extension on the far side of the table to hold the far piece. There are different things you can use. The easiest is to buy 1 or two table saw roller stands. They are adjustable to meet the height of your saw so you don't have to try to hold the wood down to cut those last couple inches. building/finding a table of the same height and putting it behind the saw would work in a similar fashion.
Cutting it in a straight line, the simplest is lots of practice! :). Since I am guessing that paying lots to get a decent sized saw or getting a table extender are out of the question (I want an extender but ~$800!) so...
If you have a router with a straight bit, try and cut you pieces outside the line then use the the router, a guide board clamped down and a straight bit to give it a nice clean straight cut to the line.
Having a circular saw (also commonly called a Skil saw) and saw horses would actually be my recommended tool over a contractors saw for sheet material.
Last but certainly not least, a second person. They can help guide from the far side of the saw until you get it started, then they just help hold as you guide and push.
Then there is how straight are you looking for? even a regular table saw with a fence, still needs practice cutting straight on large pieces with one person, one corner or the other tends to want to move the wrong way, making a wavy line.
Actually the Last one is to have the big cuts made on your material at Home Depot or where ever you buy it. I think home depot gives 1 or 2 cuts for free. then a cheap fee for more. So cut the big ones down, and do the smaller cuts at home.