Not having any psychic ability... here's how I'd do it.

Genuine psychics can apparently rely on dead people communicating directly (though rarely clearly) with them. I've had experience of listening to an Edison wax cylinder recording made from 1888. It was very muffled so I expect hearing from people who've passed over is somewhat similar. I'm also not certain how you 'hear' from someone who's died as their vocal cords won't be working, but such is the mystery of communicating with those who are no longer here.

I don't have the gift of speaking with the spirit world so I'd be unable to do that without some sleight of hand. Here's how I'd give people the impression that I can do it though - it's almost the same thing I think. Obviously this is a thought experiment and I won't actually tell people that I can talk to their departed loved ones as it seems cruel to do so if you can't actually do that.

1. Local and national newspapers' archives (online, libraries)
First, I'd find out who's died locally within the last year. Most towns have a local newspaper and their archive is online. I'd search the name of the city / town and add 'local paper' or 'local news' and see what comes up. Noting the web address(es) of local paper(s) I might expand the search with something like:

inurl:localnewspaper.co.uk died
or
inurl:localnewspaper.co.uk death - and you can use Google's search features to restrict to within a particular time period.

I might also just try the name of the town and 'died' and variants of that. And of course mainstream newspapers' obituaries (almost all online).

2. If you build it they will share their data with you
Probably I'd have already set up a Facebook page or Twitter feed so that people could tell me which shows they were coming to - a few scrolls through their profiles ('Facebook creeping') might tell me if they'd lost someone (or even if their friends had lost someone) and who that person was.

Someone on Twitter might have mentioned a few months ago something about someone they'd lost and that wouldn't show up on looking at their current profile, fortunately Twitter's advanced search lets you go back much further in someone's tweets.

I'd probably also have a sign-up form on my website with a field for people's postcode. That tells me their city and street, and in some cases narrows it down to a few houses so I can have a good idea of where they live and perhaps what amenities are nearby (perhaps a local church, might take a wander and look at the headstones if I'm in the area). Their email address might not be very instructive (gmail.com) but maybe they'll use a work email address so I'll know where they work. If I sold things on my website I'd have their bank information too, might be able to get further info from that.



3. Advanced trolling
There used to be a magazine psychic who asked readers to send in a photo, name, phone number and SAE (stamped addressed envelope). I wonder how many of the people writing in understood what information could be gleaned from that, though this was a few years ago in the earlier days of the internet when finding info out would have taken a different set of research skills.

Another person, Peter Popoff (an evangelical preacher / 'healer'), had a clever technique of (a) getting people to fill out prayer cards at his events with their name, address and afflictions and (b) getting his wife to communicate this to him by an in-ear microphone. Of course the audience at his shows didn't know about this in-ear microphone and believed that he was receiving this information through divine means.

4. Further reading
Techniques used by psychics include psychological tricks such as cold reading (making reasonable guesstimates about you from your appearance, and the things you say and contribute to the conversation) and hot reading (doing a background check on you, foreknowledge).

I might also familiarise myself with some examples of 'jigsaw identification' which shows how bits of information that are not obviously related can be used to triangulate other bits of information.