The best way to get to know strategy consulting is to apply for one of the introductory events in your country. There are usually many of those each year and there are for sure several which are specifically organized for people coming from the hard sciences. At such event you will be able to meet consultants with similar backgrounds as yourself and ask all the questions. Also, there will be general sessions on what consulting is, how consultant’s typical day looks like, etc. Usually these events include some interactive things as well, for example solving the business cases in teams. The good thing about events is that you can apply as many times as you want and if you are invited and show yourself positively at the event, you get automatically invited for an interview also. So, go to the websites of McKinsey, BCG and Bain in your country, see what event calls are out and apply :)
But of course, also try to activate your network and see whether you have friends of friends who currently work at the MBB or have previously worked there. So that you can ask all the questions in the informal atmosphere.