Can people create a country?
Anyone can declare a country, the trick is in getting other countries to recognise your country as legitimate. While there are some international treaties covering this, what it really comes down to is what relationship do you have with those countries you want to recognise you.
For example, almost everyone agrees that Australia is a country, but few people recognise the legitimacy of Transnistria, despite it having land, a currency, a parliament, and other institutions associated with nationhood.
TL;DR Yes, people can create a country, but no-one may care.
Firstly, wasn't Israel created by a British politician Arthur Balfour? Secondly, as Kevin Thorpe alludes to micronations - these are Principalities - like Monaco, Andorra, Liechtenstein etc., created by a section of the community having a slight difference with their neighbours. The next one could be Catalonia regaining its principality status.
You'll be looking at a micronation. Basically declare that you are one and get other established countries to recognise you.
For further reading How to Start Your Own Micronation