How do you say “I don’t know how to [verb]” in Japanese.?

1. structure: verb stem (for the normal forms) + kata, 方 (the way) = how to [verb]. The resulting structure functions like a noun, and normally takes the appropriate particle.

2. don't know =

a. wakarimasen - normal politeness, for use with most people.

b. wakaranai - plain politeness, for use with family, close friends, sometimes equals of the same age group (students, for example)

c. both also mean - don't understand.

d. ga - is the normal particle for direct objects of wakaru (instead of the normal "o", or "wo", depending on the romanization system you use. Both pronounced as "oh". )

3. note: shirimasen (normal); shiranai (plain), also mean -- don't know, and have similar meanings to #2, but the negative shiru forms imply that you are unaware or have never heard of something, or might imply you don't care (which can be rude in some circumstances). The negative wakaru forms imply that you tried to understand something but couldn't, and is neutral (not sometimes rude).

4. Japanese is an extreme pro-drop language. You do not include a pronoun, any pronoun, when clear from context. So normally, "I" would not be translated, when clear from context that you are talking about yourself. It is often assumed when you start a topic without specifying it that you are talking about yourself (in a statement). In a question, it's assumed you are talking to the listener (you).

5. There are many ways to translate "I", depending on the level of politeness, and the age & sex of the speaker. Most students learn "watashi" first, but in modern Japanese that can be extremely polite for a man (but normal for a woman).

6. Your two examples:

a. swim = oyogu. stem= oyogi. how to swim = oyogikatta. So:

oyogikatta (ga) wakarimasen (normal politeness). ga - is often omitted with wakaru.

泳ぎ方がわかりません

b. use = tsukau; stem = tsukai; how to use = tsukaikatta. So:

kamerano tsukaikatta (ga) wakarimasen.

カメラの使い方がわかりません。

note that since tsukaikatta is now a now, to connect camera with it, you use the particle "no" (of), which turns camera into an adjective. (the way to use of a camera // the camera's way to use), instead of wo/o as the direct object of the verb "use".

7. also note (I am uncertain how familiar you are with Japanese), that "vowel" verbs simply remove the -ru ending from the plain affirmative form instead of also adding an -i like the "consonant" verbs used in your two examples). example: eat = taberu; stem = tabe; how to eat = tabekata.