Welcome to Android Central! Not all Android tablets are certified to use Google Play Store, especially the ones from lesser known manufacturers. Are you saying that you have Google Play Store but are unable to install an app from it, or are you saying that you can't get Google Play Store for your tablet?
If you can't get Google Play Store at all on your tablet, then I suggest installing the Amazon Appstore instead. It has more or less the same library of apps. You can install it by using your tablet's browser and going to this address:
Install Amazon Appstore. Then follow the instructions.
If you can't install Amazon Appstore (which might be a problem in certain countries), then try other app stores like GetJar or SlideMe.