Firstly, why? If you do want to transition from wearing the traditional type of running shoes to the more minimalist running shoes, then make sure you are doing it for the right reasons. Don’t do it for the hype and marketing and all the claims that get made for it. The science is clear, in that the injury rates between those who run in minimalist running shoes compared to the traditional running shoes is the same and there is a higher risk for injury during the transition to the minimalist shoes, so is it worth it? There was a lot of hype around this a few years back and it never lived up to the hype and expectations. Minimalist running shoe sales make up less the 0.5% of the running shoe market, so runners have voted with their feet when it comes to minimalist running.
If you do want to transition to minimalist running shoes, then it is going to take a while. You can not just buy a pair and go for a long run today. You will mostly likely get an injury doing that and a lots of runners have done just that. What you are going to need to do, is do it very slowly and gradually and give time for your body to adjust and adapt to the different loads that will be applied. Just how fast you can move through this process will depend on may factors such as your age (eg younger can do it quicker), how heavy you are (eg those who are heavier need to take more time) and if you have done any cross training (eg those who do more, will probably be able to go quicker). Initially you should just go for walks in these shoes, then very short runs, interspersed with runs in your usual shoes. Over time you slowing increase the length and frequency of the runs in the minimalist shoes and decrease the use of the traditional running shoes. Please do it carefully. Think months rather than weeks to achieve this.
Oh, and I personally do not think that there is anything wrong with barefoot running or using minimalist running shoes as long as people do it for the right reasons and do not exsposue nonsense and nonsensical science to try and defend what they do and convince others to do it.