To form the first and second declension, you simply cut off the -re at the end of the 2nd Principle Part (2PP) and add on the endings. For the 3rd/3rd-io and 4th declension, you must use a different technique. Think of them as a different set of endings - group 1 and 2 in your mind, and group 3 and 4 separately.
Under the cut I’ll explain how to form 3rd/3rd-io and 4th declensions in the present tense, and in both active and passive.
Active
Let’s take the verb lego, legere, legi, lectus (to read) as we work through how to form the 3rd declension.
Now, for present active, you always use the first principle part for singular 1st person. Therefore, “I read” will be lego. 1st Person, Singular, and Active will always be the 1st principle part. Now, I will explain how to get the other forms down.
For present tense, these are the steps we’ll use.
Cut off the -ere in the infinitive.
Add i (except in 3rd person plural - there, use u)
Add active endings
Note that instead of cutting off the -re, you cut off the vowel plus the -re on the end of the 2PP. Also note that for only 3rd person plural will the vowel will be u instead of i in the second step. You’ll notice the u will be present here in the 3rd-io and 4th declensions as well! So, let us form the verb lego for 2nd person singular.
Legere
Legi
Legis
Legis is our 2nd Person Singular Present form of lego! This means “you read.” Now, let’s do 3rd person plural so we can see how to use the u.
Legere
Legu
Legunt
The 3rd person plural is legunt! This means “they read.” Now, here is a chart of all of the present active forms of lego:
For 3rd-io and 4th, we use mostly the same steps, although the 4th declension already has the i when you cut off the -re. However, for simplicity, we will use the same steps, as the 3rd and 4th declensions are grouped together in how they are formed.
The only difference is that on the 3rd person plural, we use iu instead of just u.
Therefore, the 1st person plural active form of audio is audimus. Here is a chart of audio:
Passive
The ending for 1st person singular in passive is -or. However, the 3rd-io and 4th declensions will have an -i in front of the -or. So lego will become legor, but audio will become audior.
To make the other passive persons and numbers, we use the same steps, but with passive endings:
Cut off the -vowel re
Add i/u/iu
Add passive endings
For an example, here’s facio, facere, feci, factus (to make or do) in 3rd person singular
facere
faci
facitur
And so the passive present singular 1st person is facitur.
"SCIENTIA POTENTATUS EST" "Knowledge is power" Potentatus, a nice masculine fourth declension noun, does mean "power". Making this technically correct. Potentatus, however, seems to be very uncommon in Classical Latin, appearing only once each in Cicero, Caesar, and Livy according to the Lewis and Short. A PHI Latin (latin.packhum.org) search only comes up with Caesar and Livy, plus an example from Justinian. Some of us might be more comfortable with the more popular "potentia", as in "Scientia potentia est." H/t to Thomas Schmid (@th_schmid) via Twitter for this found Latin.