How to learn different kanji readings?

I've been studying Japanese for about a year and have recently started working on learning kanji - both reading and writing. I have decided to use the Japanese grades order, and have been using the KanjiBox app (with KanjiDraw extra) and practice sheets for writing by hand.

I am currently doing grade 1 kanji, which by now are no problem to write either by hand or in the app, based on the meaning or converting it from hiragana word. However, the reading is still an issue - for most kanji, I can only remember 1 or 2 readings, which I know from practical use (my vocabulary is already more advanced than my kanji knowledge), but can't remember all readings therefore I have trouble when seeing a kanji in text - I never know how to properly read it out loud. I've been struggling with this for a while but somehow, I keep forgetting different readings.

Has anyone else had this struggle and found a way to overcome it? I am quite confident in writing grade 1 kanji already but I'm just not progressing at reading. Any advice?

Most kanji have two different readings: an On-yomi 音読み and a kun-yomi　訓読み. From what I remember--and I might be wrong--the on-yomi are the readings that came from Chinese. Obviously that can't apply to all Chinese, but I believe 愛　and 茶 are at least the same in both languages. Kun-yomi on the other hand were made in Japan.

Take the kanji 時, for example. It has two readings; the on-yomi is ジ, and the kun-yomi is とき. As I am sure you know, there are two ways to say time 時間, a combination of two on-yomis, and just plain とき

これを説明する時間がない。
日本語を話すときに緊張してしまう。

I would maybe say that 90%, if not more, follow this pattern. This seems to be especially true from n3 forward.

When I was learning kanji I wrote the on-yomis in katakana and the kun-yomis in hiragana. I memorized them, and when I came across a word I didn't know, I would try the method I stated above: if there are two characters together to make a word, use the onyomis; if there is a single character alone, use the kunyomi.

説明 is a combination of two onyomi's. 説く and 明るい are kunyomis. It's kinda like how な adjectives aren't "real" adjectives; they're nouns. You have to use a な to bridge the gap and make them adjectives. In the same manner onyomi's aren't strong enough alone to make a word; they have to be paired up with other onyomi's to function.

底、低、邸、抵　Notice anything similar? Kanji that same to have the part in them sometimes have the same on-yomi. In this case, they are all pronounced テイ. But becareful, 容　浴、谷 look alike, but all have different on-yomi.

I think it's incredibly important to know that on and kun-yomis exist. From what a minshuku owner has told me, a lot of Japanese don't know about them per se. How true that is, I don't know.

I'm afraid that this minsyuku owner was not educated in school, unless he was joking or modest. All Japanese elementary school pupils learn and know this distinction itself, even if they don't have much knowledge in kanji.

For English speaking learners, this website might be interesting.
http://homepage3.nifty.com/jgrammar/grammar/data/kanji.htm

Which source are you using to find out kanji readings? Many of them list a lot of readings, some of which are only found in a handful of obscure words nobody uses anyway. School textbooks and similar "official" sources rarely list more than one or two readings of each type, and all listed readings are commonly used.

I would recommend learning the kanji together when you learn the vocabulary - that way you can connect the essential meaning of each kanji, the words they are used in, AND the sounds together, instead of simply trying to "memorize" the readings.

So when you learn the word "jikan" (time) you look it up to see that it is written 時間, consisting of "time" and "duration/between." Then you note that 時 is read "ji" in this word. OK. When you learn the word "tokei," (watch or clock) 時計, consisting of "time" and "measure." Then you note that 時 in this word is "to." And when you see 日本語を話すとき... then you know that "toki" is another reading of 時. And of course they all have something to do with "time."

If you want to start with the kanji list by school year, then again I would recommend learning a few words containing each of the kanji.

Reading your question again, you seem to be under the impression that after you "learn the kanji", you know the pronounciation of every word that uses them. Sorry, but that's not how it works. A work (kanji compound, kanji with okurigana, even isolated kanji) should be viewed and memorised as a separate entity, with its own meaning and pronounciation. "Knowing the kanji" can sorta-kinda give you a hint in both regards, but not 100% certainty. The only way to be sure to pronounce a word correctly or to know its meaning is to have memorised it.

Since your vocabulary knowledge is beyond your kanji knowledge (I think this is true for most westerners learning Japanese), try and learn the kanji for words you already know.

More practically, try and find things to read that are at about your level (manga, etc.), and when you encounter kanji words that you don't know how to read look them up. Try and commit it to memory as best you can in the moment, then just move on. When it comes up again and you can't remember it, look it up again. Repeat until you no longer need to look that word up. You can need read the kanji for that word.