ANSWER – I think that the best ritual you can do when greeting a new deity is one as personalised as possible to the deity you are welcoming. There is no set structure and I honestly believe even if there were the Gods would value it less than a ritual you have devised yourself based on your own research and with your own ideas and thoughts.
My suggestion is you do some reading around Hades and find out more about him as a deity. Hades was the Greek God of the Underworld so there is a real Earth connection there. This might suggest an outdoor ritual – or perhaps setting up an altar with a focus on the element of earth?
I always think the best way to build a relationship with any God/Goddess is through sacrifice, this shows them you are serious in your intentions. I’m not talking olde worldy concepts of sacrifice but the much more meaningful method of giving up your time to do something constructive and positive, putting something of value into the world. In the cases of Hades think about what it is he represents. Could a ritual take the form of volunteering to clear out a local hospital garden perhaps? He’s got a close association with dogs, how about offering time/money/support to the RSPCA? These kind of ideas do not have to replace a simple formal introduction ceremony but they add some gravitas to your intentions and will get you noticed as somebody who is genuine about developing a relationship with the Gods.
In terms of making the initial introduction, I see nothing at all wrong with making a respectful personal shrine/altar, perhaps with a picture of your chosen deity on it (doesn’t have to be anything fancy or too obvious, even a nice plant on a small table would work. If you deem it sacred, it will be sacred) - lighting a candle and stating politely your desire to make a connection. The rest as they say is in the hands of the Gods. Listen and wait to see if your voice has been heard – you will know soon enough if your interest is reciprocated.