I think that's one of difficult parts in Japanese grammars.
Basically, there are two patterns.
1. Conjugate the verb
There are several types of conjugation, for example,
"走る"(hashiru = to run)
aff.
走る(hashiru) → 走れる(hashireru, meaning "can run")
走ります(hashirimasu) → 走れます(hashiremasu)
neg.
走らない(hashiranai) → 走れない(hashirenai, meaning "cannot run")
走りません(hashirimasen) → 走れません (hashiremasen)
"食べる"(taberu = to eat)
aff.
食べる(taberu) → 食べられる(taberareru)
食べます(tabemasu) → 食べられます(taberaremasu)
neg.
食べない(tabenai) → 食べられない(taberarenai)
食べません(tabemasen) → 食べられません (taberaremasen)
"言う"(iu = to tell, to say)
aff.
言う(iu) → 言える(ieru)
言います(iimasu) → 言えます(iemasu)
neg.
言わない(iwanai) → 言えない(ienai)
言いません(iimasen) → 言えません (iemasen)
2. In the case of a verb ending with "する(suru)", replace "する" with another verb "できる(dekiru)" and conjugate "できる" accordingly, for example,
"説明する"(setsumei suru, to explain)
aff.
説明する(setsumei suru) → 説明できる(setumei dekiru)
説明します(setsumei shimasu) → 説明できます(setsumei dekimasu)
neg.
説明しない(setsumei shinai) → 説明できない(setsumei dekinai)
説明しません(setsumei shimasen) → 説明できません (setsumei dekimasen)
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By the way, I will tell you a clue. If you are unsure how to conjugate a verb into a "can do" form, then just add "ことができる"(koto ga dekiru, meaning "be able to"), for example,
"買う" (kau, to buy) → aff. "買うことができる (kau koto ga dekiru)"
"無視する"(mushi suru, to ignore) →neg. "無視することができません(mushi suru koto ga dekimasen)", etc.
These expressions are grammatically correct but rather too long, so maybe your Japanese-speaking friend will teach you a shorter form such as "買える(kaeru)" or "無視できません(mushi dekimasen)" as appropriate.