The present participle is defined as the form of a verb that ends in -ing: run becomes running, sit becomes sitting, think becomes thinking, etc. According to Oxford Dictionaries, present participles are used as continuous tenses, in non-finite clauses, as nouns and as adjectives. Thus they function as auxiliary verbs, verbs-into-nouns or modifiers, but not as main verbs.
How a Present Participle Works
It's important to realize that the term "present participle" has nothing to do with time or tense. It's a designation of how the word is formed, but that formation does not limit it to present tense. In a continuous tense formation, one could write "I am resting" -- "resting" is the present participle, and the sentence is present tense because the main verb "am" is present tense. Thus, the confusion might set in -- that a present participle must be present tense.
Present Participles Don't Determine Tense
However, the same present participle can be used in past tense: "I was thinking." The main verb "was," not the participle, determines the tense. Thus, a continuous tense formation in a past-tense narrative is simple: "John was thinking about Mary" or "Alice was running home" or "She was drinking too heavily." Incidentally, the present participle lends itself just as easily to future tense: "One day, John will be thinking about Mary more and more."
Any Usage Works
By the same token, the other usages of present participles are perfectly appropriate in past-tense narratives. In non-finite clauses, present participles are verbs in a dependent clause that joins to an independent clause: "Sitting alone, I am perfectly content." Change the main verb, and it's just as easily past tense: "Sitting alone, I was perfectly content." Even used as nouns or adjectives, they are appropriate in past tense: "That was good thinking on her part" and "The sinking sun was beautiful."
Present Participles Work Anywhere
A writer can successfully use present participles in past-tense narratives, as long as he remembers that the word "present" in the "present participle" is its form, not its tense. A present-tense sentence that uses a present participle becomes the past tense through the main verb of the sentence, not through the participle that accompanies it as auxiliary verb, verb-into-noun or modifier.