In general we dintinguish between verbs that take a direct object (without the intervention of a preposition) and those that do not.
Appeler belongs to the first category (takes a direct object; accusative) whereas téléphoner belongs to the second one (takes an indirect object; dative).
J'appelle mon amie. I call my friend.
Je l'appelle. I call her.
Je vais téléphoner à mon amie. Je vais lui téléphoner.
Many French intransitive verbs may take an indirect (dative) object as in English. The dative form of nouns and some pronouns is obtained by adding à; other pronouns have special dative forms.
Il parle aux étudiants. Il leur parle. À qui parlez-vous ? (He speaks
to the students. He speaks to them. Whom were you speaking to?)
A number of French verbs require an indirect (dative) object, whereas their English counterparts take a direct (accusative) object. E.g.:
Repondre à = answer; ressembler à = resemble; se fier à = trust ;
obéir à = obey
Many French transitive verbs, which take a direct object, may take an indirect object as well. E.g.: donner, offrir, montrer, enseigner:
Je donne le livre à mon frère => Je le lui donne.
Il enseigne le français à sa femme => Il le lui enseigne (i.e. à elle;
reprise)
Il leur offrit un cadeau. He offered them a present.
Many transitive verbs may be constructed with the preposition à without representing the dative, but some other idea, such as motion to, direction of thoughts, etc. This distinction (i.e. between dative and non-dative) affects the form of some pronouns.
Verbs of motion may be constructed with non-dative à:
Il va à l'église (Il y va). Elle y courut. L'enfant est venu à moi.
But à with verbs of motion when used figuratively is dative:
L'idée leur est venue. The idea came to them.
Cela lui convient. That suits him.
Cette robe lui va. That dress suits her.
À is also not dative after, for example, a
appeler à; être à; comparer à; faire attention à; habituer à.
Ce livre est à lui. Il ne fait aucune attention à eux.
A number of other French verbs are constructed with non-dative à including
arriver à, parvenir à; croire à, jouer à, s'intéresser à, manquer à, penser à, songer à, renoncer à, avoir affaire à.
Il faut renoncer à elle. (Il lui faut renoncer is erroneous).
Je pense à Pierre. Je pense à lui (Je lui pense is erroneous).
Je m'intéresse à elle.
References:
1) A French Reference Grammar (H. Ferrar).
2) A Student Grammar of French (M. Offold).
Grammar glossary:
1) http://www.languageguide.org/french/grammar/
2) http://www.beechencliff.org.uk/files/ml/german/prod_2/atm/common/grammar_section.pdf