deponents

[elduce]

Deponent verbs have no active spelling at all? This makes it difficult to figure out what conjugation sort they are. I can tell hortari is first conjugation. Did these verbs ever have an active spelling, and how did anyone figure out these passive verbs meant active action?

Gratias

[benissimus]

Deponent verbs have no active spelling at all?

Usually the case. Some verbs that are deponent have corresponding active verbs, but do not mistake these to be the same verbs. verto, vertere, verti, versum means "to turn (something)" and is transitive; vertor, verti, versus sum means "to turn (oneself)" and is intransitive. "I turned my chair to face the sun" would be verto but "I turn to my friends" would be vertor.

This makes it difficult to figure out what conjugation sort they are. I can tell hortari is first conjugation.

There should not be any trouble once you have your passive forms well memorized. I remember the awkwardness that existed at first too. It may take some getting used to, but the first principal part will still be the first person singular present indicative but passive in form, the second principal part is still the infinitive but passive, and the third principal part is still the first person singular perfect indicative but passive again.

Or, if you prefer:
1st conj. verbs: -o, -are as in laudo, laudare
1st conj. deponents: -or, -ari as in hortor, hortari

2nd conj. verbs: -eo, -ere as in moneo, monere
2nd conj. deponents: -eor, -eri as in tueor, tueri

3rd conj. verbs: -o, -ere as in duco, ducere (-io, -ere as in capio, capere)
3rd conj. deponents: -or, -i as in vertor, verti (-ior, -i as in morior, mori)

4th conj. verbs: -io, -ire as in sentio, sentire
4th conj. deponents: -ior, -iri as in molior, moliri

Did these verbs ever have an active spelling,

Most of them originate from the middle voice, which merged with the Latin passive. Greek on the other hand preserved its middle voice and thus is heavily involved with this type of verb. You may notice in your studies that many Latin deponents express an action that affects the speaker in some way, either by being intransitive or simply expressing reflexivity by their meaning (as mori "to die", uti "to use; lit. to benefit oneself", moliri "to struggle", minari "to (move) threaten(ingly); to jut outward", verti "to turn (oneself)", gradior "to (take a) step", dominari "to dominate; lit. to be master") - this is the remnant of the middle voice meaning.

and how did anyone figure out these passive verbs meant active action?

The language has never stopped being taught and spoken, so no one has ever had to go back and decipher it all, if that is what you mean. If the language wasn't ever lost to begin with, then there have always been people who knew that deponents carry an active (err... middle) sense.