You should certainly follow Dave's link, but if you need some specific help now, we need to know a lot more if we're going to help you. Please provide answers to the questions listed here: "FAQ: What information should I provide when asking a question on this forum?"
AE CC 2014 release - up to date
Windows 7 PRofessional
Inter Core i5-3470 CPU, @3.2GHz
4.00 GB RAM
HPCompaq Pro 6300 SFF
NVIDIA NVS 300
Intel HD Graphics
2 HP Compaq LA@306 Wide LCD monitors
no external drives
no third party hardware, or effects or codecs
I open AE, open the project and then try to play it by hitting space bar and it plays extremely slowly - about 1 frame every 2 secs or more.
That is a very small amount of RAM for After Effects. 2 seconds per frame is not an unusual amount of time for certain kinds of compositions; since we know nothing about your composition, we can't comment on whether this is normal for this composition.
4 gigs of memory? Thenk about getting that up to 16 gigs. Seriously.
Among the many things you'll learn in that Getting Started link is to keep your fingers off the space bar. AE can NOT play anything. It doesn't work like a video editing application.
So how do you see your stuff? RAM Preview -- hit the zero on the numeric keypad, wait while AE renders as much of the comp as it can to memory, and then plays back out of the memory... and because you don't have much, you won't get much of a preview.