How do I know when past participles should agree?

In French the past participles of direct verbs have to agree with the gender or number of their object. For example, ‘I saw him’ translates as ‘je l’ai vu’, but ‘I saw her’ as ‘je l’ai vue’, and 'I saw them' as ‘je les ai vus’. This is the rule for direct verbs — that is, verbs that aren’t followed by a preposition, like ‘à’. Examples of indirect verbs are ‘téléphoner à’, ‘écrire à’ and ‘parler à’. They are called ‘indirect’ because the verb does not ‘act’ directly on its object, because there is an ‘à’ in between: ‘écrire quelque chose’ means something different from ‘écrire à quelqu’un’. When these verbs are used in the perfect tense, their participles do not agree with the gender or number of their object. For example, to say ‘I spoke to her’, we say ‘je lui ai parlé’ and NOT ‘je lui ai parlée’; to say ‘I telephoned them’, we say ‘je leur ai téléphoné’, and NOT ‘je leur ai téléphonés’. If you’re having trouble remembering whether the past participle should agree, just think how the verb would appear in its infinitive form: if it would normally be followed by an ‘à’, it’s an indirect verb and so its participle shouldn’t agree; if the verb would normally just appear by itself, it’s a direct verb and so its participle should agree.