Hi!
In Japanese, if you want to express "the potential or capability to do something", there are basically 2 ways:
1) Using the potential form of a verb. Your example: yomu --> yomeru, yomimasu --> yomemasu
Here the basic sentence pattern is:
(x) ni (y) ga + verb (in potential form); where (x) is the subject and (y) is the direct object.
We often don't state " (x) ni " if the subject is clear or known. You cannot change (ga) to (wo) when using the potential form.
O "correct" watashi (ni) wa hiragana ga yomemasu or hiragana ga yomemasu
x"incorrect" watashi (ni) wa hiragana o yomemasu or hiragana o yomemasu
2) using the expression: verb (dictionary form) + koto ga dekimasu
Here, since we're using the dictionary form of a verb, you can use the particle (wo).
Example: hiragana wo yomu koto ga dekimasu "I can read hiragana"
You can use either forms to express the same idea. But it's more colloquial and less formal to use the potential form of the verb.
Hope that helps.