Rusmania can plan your BAM trip as you like it. You just need to decide where to start and where to end, and all the stops you would like to make in the middle. You will need to make a stop in Tynda to change trains if you want to complete the whole route as there is no one train which runs between Tayshet and Komsomolsk-on-Amur/Sovetskaya Gavan.
You can travel along BAM from west to east or from east to west. It doesn’t really matter which direction you choose, but the west to east option is a little more common, meaning that there might be less people on the east to west option.
You have two options for travelling to BAM, by train or by plane. From west to east you can get a train to Tayshet where the Trans-Sib meets BAM. There is even a train from Moscow to Tynda, stopping on the way at various cities along the Trans-Sib and then the western section of BAM. From east to west there are trains from Vladivostok to Sovetskaya Gavan via Komsomolsk-on-Amur.
If you want to fly to BAM the nearest major airports are located in Krasnoyarsk and Irkutsk at the western end and in Khabarovsk at the eastern end. There are also smaller airports in Bratsk and Nizhneangarsk.