Whenever you wish to imply that a verb “is possible”, that it “can” or “has the ability” to do something, you take the verb and modify it using some rules based on the type of verb (ie: u-verbs, ru-verbs, irr. verbs)
Most conversions are pretty straight forward, some are a bit more complicated.
For ru verbs: Drop the final ーる and add られる.
Example: 見る→見られる
For u-verbs: Drop the final ーう and add ーえる.
Example: 行く→行ける
Notice how the く reverts to to け. The “-u” in く (ku) is replaced with “-e” making it け (ke)
Likewise, 話す→話せる
す(su) has it’s “-u” replaced with “-e” making it せ(se).
Also note that る is added to the end as well. This る changes the verb into a ru-verb essentially, and allows you to conjugate them as ru-verbs.
So for example, if you wanted to write using -masu form, you could conjugate 行く as:
行けます and 行けません
You can even apply the ーんです。 to add an implication as though the potential verb were a ru-verb.
Example: 私は買えないんです。
(In debt with student loans, therefore…) I cannot buy it.
An important note is that the verbs that take the particle を can actually take either を or が when they have been turned into potential verbs. Verbs that take particles other than を remain the same however.
Another important note is that する is a bit special.
It usually takes が almost all of the time, and when it’s transformed into a a potential verb is: できる.
くる is also a bit special. It ends up becoming こられる — irregular verbs usually have these kinds of special cases though.
Below are some great charts to study and familiarize oneself with the potential verb transformations.
One last note, is that because the ru-verb variation of the potential ends up usually being longer than the original, many people in Japan don’t really bother saying the ら in the ーられる of the potential verb.
It’s not considered standard speech though, so maybe among friends or people you feel you could talk very casually to would work best for not needing the ーられる and can instead opt to use ーれる for ru-verbs to potential verbs — but otherwise if you’re not sure, then perhaps using in it’s entirety (ーられる） would be better.
Images (Tables) Source: Genki II: Elementary Japanese [Second Edition]