How to build a concrete patio
Okay so you're looking at 2 cubic yards of concrete (cement is a component of concrete). That is a hellovalotta concrete. If you have no experience with it, that is too big of a project to start with. Secure some experienced help for the pour. This is not optional seriously concrete is not hard to do, but you do not give it a try fingers crossed. Even if you have to pay a general laborer with some experience it will likely save you from having to rent a large breaker and a 10 yard bin. 

Preparing it is a different story. Excavation of the work area is not too difficult, takes a bit of time and elbow grease and needs to be done fully before the truck arrives. They bill by time and material usually.

Also have your experienced ringer come an hour or two before the truck to ensure it's ready. 

You will almost certainly not be able to match the finish or colour of the existing pad but if that's a problem, jewel stone or some other finish across both can correct that. An expansion joint is recommended. It's available at hardware stores and building suppliers. At the seam drilling rebar dowels into the side of the existing pad will help mitigate any uneven heaving. For a pad that size I'd recommend renting a power tamper and tamp the soil before laying a good 4" minimum of 3/4 run gravel. Then tamp the gravel. Your form will need to be nearly perfect and free of movement. Concrete is much heavier than water and the pressure 5-6" high concrete will make is enough to distort a poorly secured 2x4. Any defects in the wood will transfer to the finished product.

For the rebar grid you can use wire mesh, it's a 4x8' sheet with 6x6" squares. These need to be laid down on stand-offs so the mesh is approximately center of the slab. You can tie it together with zip ties if you can't find the hook loop wire ties that are made for tying rebar.

For the difference in price and the additional strength use 2x6's or even 2x8's you only need four 8' lengths be careful to get very straight pieces free of cupping and bowing.

Finishing with a 2x4 is difficult for a pro to do. You may want to look into a pole trowel.