I would google the transport for London site and if using a phone that does apps, see if they have an app. It has an walking option but I am more likely to just use an online map and check out their time compares to what I actually use, for which I use google maps.
Besides I usually have a paper map with the tube lines printed over the map as well as the streets, which you can buy out of a machine at some tube stations, and looks a bit like this. There are versions with the bus routes as well.
Armed with that I am ready to work out a route as well as be confident on walking in London and find my way around when underway.
I know that I would spend the whole day in each of these museums, and want to get back to get more the next time I have the option, I would not combine them myself, but if you only want a visit to see what all the talk is about, combining the Natural History Museum, V&A and the Science Museum is easy, as they are all in the same small area, the British Museum and Tate Modern are not as close together but they are certainly within walking distance for me. But I walk a lot when exploring London.
As I do not know what you find acceptable in walking, I would suggest to take the Circle line to South Kensington Underground Station, from there the route is well signposted to each of the museums in the area. Whether you want to walk on the way back may depend on how much you walk within the museums.
To the British Museum the planner shows several options (and if you only get one you can chose the fewest change option or the least walking option or the bus only option) so you can suit yourself.
But the best thing for you is to learn to use the underground and bus maps. One glance at a map may show you way more than several written out route schedules.