Anomalous life readings
“I think we’ve got something, sir,” Piett informed him. “The report is only a fragment from a probe droid in the Hoth system, but it’s the best lead we’ve had.”
Unimpressed, Ozzel snapped, “We have thousands of probe droids searching the galaxy. I want proof, not leads!” But Piett wasn’t finished. He added, “The visuals indicate life readings.”
“It could mean anything,” Ozzel said, growing impatient with Piett. “If we followed up every lead…”
“But sir,” Piett interrupted, “the Hoth system is supposed to be devoid of human forms.”
—The Empire Strikes Back (Junior Novelization)
This serves as a strong sign that something untoward is going on. As Piett later says, it could be smugglers, but Darth Vader is pretty confident that it is Luke.
They have images of Rebel snowspeeders
Yes, sir,” Piett said slowly, choosing his words with caution. “We have visuals. The system is supposed to be devoid of human forms. . .” But Vader was no longer listening to the captain. His masked face turned toward an image beamed on one of the viewscreens—an image of a small squadron of Rebel snowspeeders streaking above the white fields.
—The Empire Strikes Back (Novelization)
From the script, as well:
Vader moves to a large screen showing an image of the Rebel snow base. Rebel speeders can be seen approaching the base in the distance.
VADER: You found something?
PIETT: Yes, my lord.
It's unclear whether the snowspeeders have any markings or design elements indicating their Rebel affiliation, but they may. Alternately, the fact that a full squadron of speeders is present might tend to rule out smugglers, who might tend to have fewer members.
In that vein, the size of the base might be a clue as well that there is something more than smuggling going on. Also, the picture in the film appears to be of shield generators, which should be a dead giveaway that it is a military facility.
The Force
True, Darth Vader's skill in the Force was not enough to simply pull the location of the base out of thin air.
As Admiral Motti says:
ADMIRAL MOTTI: Don't try to frighten us with your sorcerer's ways, Lord Vader. Your sad devotion to that ancient religion has not helped you conjure up the stolen data tapes, or given you clairvoyance enough to find the rebels' hidden fort-....
But it is possible that, with additional information (such as a picture of the Rebel base), the Force could provide him with sufficient intuition to know whether it was the right place or not.
“That’s it,” Vader said with conviction. “The Rebels are there.”
Admiral Ozzel saw nothing on the monitor that specifically indicated a Rebel presence, and he did not believe in expending time and energy on a mere hunch.
—The Empire Strikes Back (Junior Novelization)
This is also the impression conveyed by the The Empire Strikes Back: So You Want to Be a Jedi?, in which Vader can "sense" the presence of Luke and the Rebels, as mentioned in another answer.
Of course, Luke Skywalker was also at that base (which he was not in the previous case), and Force users have been shown to be able to sense the Force in others, albeit inconsistently.