Never use plywood for a deck - or for that matter - any outside structure that will get wet.  Plywood is fine as long as moisture is not allowed to infiltrate it, but when that happens, the 'plys' (multiple layers of wood laminated together) will separate and become an real mess.

For a deck, the best wood to use, if you can afford it, is cedar.

Its the most expensive (wood) material you can use but best by far.

It is inherently able to withstand issues of rot, mold, fungus and insects.

Some choose to treat the wood which will maintain the wood look, but if its simply left to the elements it eventually takes on (to some) a pleasing silver-grey hue.

Alterntively, a good pressure treated lumber can be used which is less costly.

As for the saw, any good (cross cut) hand saw works, but if you've a lot of cutting then a circular saw is advised.

Most building supply stores have all the information, parts etc. you will need.

Have a look at what others have done to get some ideas as to what you would like.

Once you have the basic platform, you may wish to have railings, a hand rail if there are to be steps and the 'look' that you want that fits into your decor and the architectual integrity of the building the deck is located next to. 

Decks can also be built out of recycled plastic that is now sold for that purpose.  This is the most expensive option.  It also requires the least maintenance - for example, its color fast and never needs painting.

It is best to use screws specifically designed for the application that will not corrode.  Nails may be cheap but are not the best.  They definitely will rust and cause ugly rust stains.