Today we are using electronic tuners and know everything about frequencies but in the past, like before the 16th century, how could people tune their instruments? Did they tune them to specific frequencies? What reference did they have? Did they use some kind of instrument?
Never mind the 16th C., even in the 1960s, reference points were not considered necessary by some recording bands, particularly those with only guitars and basses to go with drums! As long as one of the guitars was in tune with itself, the others used that as a datum point.
Back in the 16th C., there was not a great deal of travel involved with musicians; making music was parochial, so the need for an industry standard such as we rely on nowadays wasn't needed. With easily tuneable (?!) instruments, i.e. lutes, as long as they were in tune with other no-so-easily tuneable instruments, it wasn't really an issue. And tuning was such that some instruments sounded better in one key (no 12EDO yet).
Tuning forks, as already mentioned, were around from the beginning of the 1700s, so there was no 'official' datum point anyway at a time previous.
Back in the '60s, I used to drop a house key on a hard surface, which gave me a reference to keep my guitar in tune, and I guess similar ideas were used by instrumentalists who were fastidious enough to keep their instruments on pitch.
So, basically, everyone would, as previously said, tune to whatever instrument sounded right, but was the most difficult to alter anyway,.
In the case of the lute, a common practice was apparently to "tune the treble string as high as it will go without breaking, then tune the remaining strings in accordance with the first." (source). This of course depends on the diameter of the string, the construction of the (gut) string and the size of the lute. Lutes were made in fairly well standardized sizes (source), which suggests that the instruments were not necessarily tuned to any reference pitch, but just so the top string (on which a lot of the melody is played) sounds good and the rest of the strings tuned to match (in some particular temperament). Presumably a group of players would tune according to the top string of all the instruments that was closes to breaking? [caveat: I am not an expert on this topic!]
ETA: Lute players (especially baroque lute) spend half their lives tuning their lute, and the other half playing out of tune ;o)
Tuning forks? References varied a lot locally, but of course the local church organ would be one point of reference. But organ builders/tuners would be carrying around their own references.
I know you asked about prior to the 16th century, but...
I've never known a rock band that carried a tuning fork.
Right up to the 1970s you would simply tune to 'whoever sounded about right already' unless there was some external reference like a piano in the building - & whether that was right or not was still questionable.