Now it's not about the tool, it's about the pattern you're going to use, first of all, you have to create personas, if you have at least 1 solid persona you would know better what to change in each variation, it's better to make 1 change per variation to be able to track what works better and then add another enhancement, for example, in variation 1, change the color of the explanation text or the "what is your website" text, in variation 2 increase the size of the same text with its control color, when 1 of them wins, make another change and test again, because 2-3 changes per variation would limit your insight, you might have a winning variation with 2-3 changes but you'll never know which (of the 3 changes) led to this win.
so you have to set a persona, choose a tool, set the targets. logically, you're going after conversions, and decreasing bounce rate, these are the 2 goals you have to set before getting started, and for the persona, let's say your audience is 18-25 males who care about cars and mid-day hangouts, you might need to experiment with making a variation with an attractive image above the fold with really nice looking call to action button, and in variation 2 you try no image but a great emotional text with really evident signup/login links, now when 1 of these win you make 2 variations of it, and so on.
now for the tool to use, try Visual website optimizer, visualwebsiteoptimizer me and my team use this one and we're still experimenting with it. it allows you to test many variations live and divide the percentage of users between them, you just have to add a code to your database.
It works for testing homepages and any internal page as long as you have perfected URLs.
What other teams use is google website optimizer which is a handy tool to test homepages; it provides A/B experiments and multivariate experiment which compares the performance of content variations in multiple locations on a page. Let me know if it worked for you :)