That's a rather non specific and vague question. But you asked to be steered in the right direction...so I'll tell you not to try and run before you can walk. Try some tutorials first, and once you get to grips with the basics read some of the penetration testing frameworks that are around so you get an understanding of the entire Penetration testing process. Id also recommend you read the latest edition of Hacking Exposed - it has a good overview of the steps required to access a system via "hacking".
I should probably inform you that regardless of the fact that you apparently have "ethical approval" to hack your home network systems, your ISP might not like you sending attack traffic over their network to your systems. In addition, whatever network you launch your attacks from (since you wont be able to launch external attacks from your own network) may not like it either. Be prepared to face the consequences of your actions if you decide to go ahead with this.
Personally Id suggest confining your attack traffic within a test network, and NOT sending it via the Internet.
Anyway, what do you expect to prove by this? That home networks can be hacked? I think that everyone already knows this by now. Did your college actually assign you a project to hack into a network, because that seems like a recipe for disaster?