I assume as you asking this question you are not a programmer and you don't know the very basics of opening a website and its lifecycle. Before opening the website you must know some facts as a website owner like Domain, Hosting, Web Server, Popular programming languages, and frameworks for your purpose. you can search on google about them
Well, opening a website nowadays is very easy. You can adopt one of these following
1. By using opensource/free cms:
This will cost-saving and time-saving. This will give you a built-in admin panel. There are some good cms available for the question-answer system like phpbb, bbpres, mybb, question2answer. you can use wordpress or joomla for this purpose also.
But if you have to add more features or custom features you need to know about the programming language used to your cms, database structure or you can higher a developer for this.
2. By using paid cms like discourse, VBulletin.
3. By hiring web developers: This will cost much time and money but give you the most control over your website. There you can add adequate features and easily update your sites through your developers.
Here how you can open a website like this. if you want to run it for long time and business purpose then there more to come about maintenance, SEO, and security issue. This will be answered on "how you maintain protect and enrich your website?"