If you have a wordpress.COM account then this will NOT work.
If you set up a domain and host with the theme to create it then want to move it to a different domain then this is doable (bear in mind 1 license/purchase = 1 domain/website so you need to delete the first copy at some point) but can need to be done cautiously to prevent issues with file paths and name changing.
Most themes will come with documentation explaining the basics of set up.
Otherwise there are several articles on YouTube and/or Google but effectively you must have your own domain and hosting then you download WordPress and Install it here before uploading the theme purchase.
How the exact theme works is dependent on the theme itself but again documentation will have the basics.
You can use just about any theme you want and just add a plugin like http://codecanyon.net/item/wpsocialstreamer/3930883?WT.oss_phrase=&WT.oss_rank=114&WT.z_author=Powerfusion&WT.ac=search_list
Both by good authors but there are numerous strong ones there.
You could go with a more ‘multii-purpose’ style theme and just sacrifice the very ‘niche type’ features of an estate agency design
You could do it with a directory style theme like http://themeforest.net/item/listify-wordpress-directory-theme/9602611
Depending on your technical ability you will probably need some custom work done to it to ‘tweak it’ to your exact requirements but these kind of themes have the individual listing capability, contact capabilities, payment for people to list their property etc etc