The fastest way for sure is to use the internet. Instead of spending hours on the phone and walking along the high-street, you are just a few clicks away from pretty much any major insurance company in the world. You can search for them based on their reputation, or their prices, or any other criteria that you are looking for, and there are no shortage of websites to help you choose a particular insurance company. All this can be done with minimal stress, minimal hassle, and can easily be logged so you know which insurance companies you have considered, which you have chosen to avoid, and which you are interested in.
Another great advantage of using the internet is that you can get a quote in a matter of minutes. Instead of lengthy phone calls and long interviews, you can simply input your data into a short form and you'll get an accurate quote back immediately. Most decent insurance companies offer this capability these days, and you'd be surprised how accurate the quotes can be. Of course, if you have some exceptional circumstances or there is important information that the form doesn't cover, the quote won't be as accurate as possible, but it will certainly give you a fairly good indication of what you could end up paying. With such a quick way of getting a quote, you can easily rule out any insurance companies which you can see are instantly far too expensive (or even far too cheap). You can do this easily, and without the insurance company hassling you like they might do if you were talking to them on the phone or in person. You can then simply move on to the next insurance company if you weren't happy with the quote, or start the process if you were.