I have found all of my old school friends. Almost everyone leaves an online trace. We have a lovely WhatsApp group which had started with the people who had kept in touch and is now the whole year group, less a couple who were approached but were not interested.
Start with the old school. Does it have a facebook page/group? If yes, trawl back through every post for the last few years. Check each and every comment and like for every post. You'll probably find one or two 'maybes' there. Send them a private message. For the people who commented/reacted to a post, open their profile and look at their Friends list.
Keep a look out for older siblings as well. Look at the list of their Facebook friends (if you can).
You have to google using Boolean search terms. Start with the unusual names, let's say imaginary person Adonica Anderson from a Berkshire school.
Type this in the search bar:
"Adonica Anderson" AND "Berkshire"
Look at the image results as well.
If you are bombarded with information about an Adonica Anderson who is an author, type this in the search bar:
"Adonica Anderson" AND "Berkshire" -author
This will remove all results with the word author. You can add lots of -words to hone the search.
Think hard. Did Adonica study Engineering at Bristol Uni? Lots of people settle in the area they went to uni. Or did she go and do a beauty course? Or join the navy? Everything you remember can be used to hone your search. Little scraps of information gradually emerge.
If you can remember Adonica's brothers name Alexis you can google
"Adonica" AND "Alexis". This sometimes takes you to a death announcement of a relative, but it also gives you other names to search with. If you get a sniff of a definite area you can google the name with the phone area code - it can take to you a work address.
"Adonica" AND "0118" for Reading in Berkshire.
You can also limit your google search to specific sites like this:
"Adonica Anderson" AND "Alexis" site:Facebook.com
I know I sound like a stalker, but I used to do tracing for a living and only use my powers for good :-)
(If an Adonica Anderson Googles herself this could be freaky lol)
Good luck.