What exactly was John Clay attempting to do and how?

When Holmes sets a trap for John Clay and is waiting in the bank's basement strongroom for him to emerge through the flooring, the reader is shown the prize the notorious criminal is after. Mr. Merryweather the bank director tells Dr. Watson:

"We had occasion some months ago to strengthen our resources and borrowed for that purpose 30,000 napoleons from the Bank of France. It has become known that we have never had occasion to unpack the money, and that it is still lying in our cellar. The crate upon which I sit contains 2,000 napoleons packed between layers of lead foil. Our reserve of bullion is much larger at present than is usually kept in a single branch office, and the directors have had misgivings upon the subject.”

John Clay wanted to dig a tunnel and steal all 30,000 gold coins. They should be worth over $30,000,000 American dollars at today's gold prices. It would have been perhaps the biggest haul in British history, and it was worth all the time and effort Clay and his accomplish, whom he called Archie, put into it.

Clay had to find a place to start his tunnel. That was what brought Jabez Wilson to Sherlock Holmes. Clay managed to get a job in Wilson's pawnshop by offering to work at half wages. But Wilson was in the way. He and his confederate concocted a phony "Red-Headed League" to get Wilson out of the way for four or five hours a day, six days a week (everyone worked on Saturdays in those times). The inspiration for the idea came from the fact that Wilson had unusually brilliant red hair. He was very happy with his sinecure-- but suddenly the League was dissolved. He came to Holmes because he had heard that the detective would work on a pro bono basis if a case interested him. Wilson had little hope of regaining his job, which was paying four pounds a week, about four times the average London clerk's weekly wages, but as he explains:

"But I want to find out about them, and who they are, and what their object was in playing this prank—if it was a prank—upon me. It was a pretty expensive joke for them, for it cost them two and thirty pounds.”

Wilson is super-sensitive about being the victim of jokes and pranks because his red hair has made him the butt of jokes all his life. Holmes only takes his apparently petty case because Wilson's description of his assistant, who calls himself Vincent Spaulding, makes Holmes think he is really the notorious criminal John Clay. Wilson describes him as "Small, stout, very quick in his ways." These are good qualifications for a tunnel-digger. His accomplice, who poses as an official of the Red-Headed League, is also described by Wilson as small. This means they can dig a narrower and lower tunnel and scramble around easily. When they are emerging from the tunnel into the bank's strongroom, Clay asks Archie:

 “Have you the chisel and the bags?"

They do not intend to drag the boxes of gold coins through their tunnel. They will dump the coins into bags, which will be easier to drag. The chisel will be needed for breaking into the boxes. Mr. Wilson is sound asleep at this time of night--and it would be very unfortunate for him if he were to wake up and discover what was going on! The thieves would spend several hours dragging the heavy bags through the tunnel into the pawn shop cellar. Then, they would load the bags into a hired wagon and make off with them before daybreak. Holmes explains to Watson:

“Well, when they closed their League offices that was a sign that they cared no longer about Mr. Jabez Wilson's presence—in other words, that they had completed their tunnel. But it was essential that they should use it soon, as it might be discovered, or the bullion might be removed. Saturday would suit them better than any other day, as it would give them two days for their escape. For all these reasons I expected them to come to-night.”

When Watson first meets Jabez Wilson he describes him as "a very stout, florid-faced elderly gentleman." This is intended to explain why he would never venture down his steep cellar stairs to see what his assistant was doing down there. His florid face suggests high blood pressure and possible heart trouble. Holmes later describes Wilson as "not over-bright," which would explain why the two crooks were able to hoodwink him with their phony Red-Headed League and to dig their tunnel right under his nose.