Why are the present and the past participles of submit spelled with two t's?
As a rule of thumb:
If the base form is spelt with a single final consonant and the final syllable is stressed, then the final consonant doubles when endings (-ing, -ed, -er, -ist etc) are added
Final -l usually always doubles in UK spelling, but generally doesn't in US spelling. There's some variation with "s" (so "busing" or "bussing" are generally both acceptable).
A complication concerns cases where the vowel in the final syllable isn't stressed, but it still carries it's "full" quality (so common candidates are "a" or "i" in a final syllable). So for example, "kidnap" would become "kidnapped". There can be variation in such cases.
Obviously, we're only talking about consonant letters that actually represent consonant sounds (so you wouldn't write "bow" -> "bowwing", for example).
Here is a good explanation on Doubling Final Consonants. I am sure others will post the rules from some recognised entity
The general rule is when a verb ends with a consonant, it is doubled when it is preceded by a single vowel. For example, stop becomes stopped/stopping because the final p is preceded by only one vowel. By contrast, peel or reap become peeled/peeling and reaped/reaping because the final consonant is preceded by two vowels. I find that this rule is the easiest to remember.