For a moment, I thought this referred to the original paper on the first human genome, published 20 years ago. That would have been quite a feat, as most of the tools and datasets are likely not to exist anymore! But it seems you are referring to this publication from last year: The complete sequence of a human genome.
This is still a very big challenge, though. I don't think it is really worth it to actually re-run all the commands and calculations again, apart from being potentially expensive. You can, however, trace down the workflow they used to do it, and prepare a slide deck about it, as a sort of journal club. The supplementary materials document contains a good description of each step, and could be a starting point. There is also a github page, although it doesn't contain the actual code, but only documentation and references - you will have to go through the other papers to find it.
It is important to note that this article is not alone. When groups complete this type of big consortium work, they tend to publish several papers to describe different aspects of it. You can find the full list in the github page, and you will have to go through all these publications to find the one describing the assembly steps.
Your supervisor has given you a very tough task. It is potentially educative, and you can learn a lot from it - I wish I had the time to go through that paper in such detail! However, it is unlikely to give you opportunities for publication, unless you publish a commentary or figure out something smart out of it. Speak with your supervisor about this, and ask him to guide you through the process, don't let them just dump the work on you and leave you alone for six months.