You double the final consonant before -ing and -ed if:
- the word has one syllable and ends in consonant, vowel, consonant. This is the case for your verbs "put" and "stop".
Other examples: plan - planned; rob - robbed
The same rule applies for comparatives and superlatives: hot, hotter, hottest.
You also double the last consonant if:
-the verb has more than one syllable and has the stress on the last syllable: beGIN - beginning; preFER - preferred
(In British English, you double the consonant if the word ends in "l" even if the stress is not on the last syllable: TRAvel - travelled; CANcel - cancelling.)
There are one or two other helpful rules but you could start with these ones.