Describe the core elements of hangul syllables, such that a non-speaker with limited experience with linguistics can understand how to compose the symbols.
Hangul syllables consist of three fundamental elements:

Initial Consonant: The initial consonant is the first sound in the syllable. There are 14 basic consonants in Hangul, each represented by a unique symbol.

Vowel: The vowel represents the core sound of the syllable. There are 10 basic vowels in Hangul, also represented by unique symbols.

Final Consonant: The final consonant is the last sound in the syllable, and it is optional. There are 5 basic final consonants in Hangul, each represented by its own symbol.

To create a Hangul syllable, you need to combine these three elements together.

For example, let's say you want to write the syllable ka in Hangul. You would start with the initial consonant ㅇ (which represents a silent consonant), then add the vowel ㅏ (which represents the a sound), and then leave out the final consonant, since there is none in the ka sound.

The resulting Hangul syllable would be: ㅇ + ㅏ = 가 (pronounced ka).

Similarly, if you wanted to write the syllable so in Hangul, you would start with the initial consonant ㅅ (which represents the s sound), add the vowel ㅗ (which represents the o sound), and then leave out the final consonant, since there is none in the so sound.

The resulting Hangul syllable would be: ㅅ + ㅗ = 소 (pronounced so).

By combining these three elements together in different ways, you can create all of the syllables in the Korean language.
Why does the ka sound start with a silent consonant? Shouldn't it be a k consonant?
You are absolutely correct. I apologize for the mistake in my explanation. For the ka sound, you should indeed start with the initial consonant ㄱ which represents the k sound. Then, you add the vowel ㅏ (which represents the a sound). Since there is no final consonant in the ka sound, you can leave it out.

The resulting Hangul syllable would be: ㄱ + ㅏ = 가 (pronounced ka).

Thank you for pointing that out, and I apologize for any confusion caused.
Are there any online tools that can help me with pronunciation?
Yes there are a few.