For cutting decking components you will ideally have a few different types of power saw. It is not impossible with hand saws but it will take much longer and will be extremely hard work.
Cutting the deck joists by hand is not really practical as they are 150mm*50mm timber and are treated. A chop saw like this will make light work of any joists, posts or deck boards.
These machines can be hired from most hire shops and will make the job much easier. Alternatively you could use a large mains powered circular saw.
A reciprocating saw comes in handy for cutting the deck posts to length or for trimming off joists when they are in position. This is much easier than sawing by hand!
The chop saw is also the saw of choice for cutting deck boards. You can fit all the deck boards to the deck and then trim them after they are fixed using a circular saw if you like.
To get neat cuts around the newel posts like in this picture you will need a decent quality jigsaw. Cheap jigsaws are difficult to use and are great at cutting curved lines even when you are trying to go straight!
Here is how to cut out around the deck posts in a few easy steps. I have marked the back of the board in this example but you can mark either side. This is the shape we need cutting from the deck board.