How do I know when to agree past participles by number and gender?

Normally, when you're using the perfect tense with 'avoir' as an auxiliary verb, the past participle doesn't change to agree with anything. However, there are three main situations where the form of the past participle will change according to gender or number (i.e. masculine/feminine and singular/plural). You might have seen two of these before at GCSE, but we'll go through them one by one.
1) When using a perfect tense verb which takes 'être' as its auxiliary, the past participle agrees with the subject (you might know these as the MRS VANDERTRAMP verbs or a similar mnemonic). So with the verb "entrer", for example, if the subject is feminine or plural we would change the past participle: "la femme est entrée"; "les filles sont entrées"; "nous sommes entrés" (or "entrées" if we were all women). The same is true of reflexive verbs, which always take 'être', so: "elles se sont baignées".Advanced grammar point: verbs which look reflexive but have an object after the main verb, e.g. "elle s'est brossé les dents", where "les dents" is the object, aren't strictly reflexive verbs and don't behave in this way. The "se" here is actually an indirect object pronoun and "les dents" are the direct object (literally "she brushed the teeth to herself").
2) When writing in the passive voice, when something is somethinged by someone e.g. "the meeting is cancelled by the boss", the past participle agrees with the subject (here, the meeting). So in French, that would be "la réunion est annulée par le patron": since "la réunion" is feminine, you add an E to "annulé" for the agreement.
3) Finally, a rule that you might not have come across: preceding direct object in the perfect (or pluperfect) tense. When the direct object of a sentence, or a direct object pronoun, comes before the main verb, the past participle agrees with the gender of the object. This is complicated, so here's an example: "I wrote a letter" is a normal sentence which would use "avoir", so "j'ai écrit une lettre". "Je" is the subject, "ai écrit" is the perfect tense verb with "avoir" as auxiliary, "une lettre" is the direct object. If we change the sentence order so "une lettre" comes before the verb, the direct object precedes the main verb so the PP agrees with the feminine "lettre": "la lettre que j'ai écrite". The same happens every time you use a direct object pronoun in the perfect tense, as that always comes before the verb, so "je l'ai écrite" where l' refers to the feminine "lettre".