The definitions in Oxford Dictionaries Online describe some common traits of finite and non-finite verbs in English, but they overlook the key differences that you'd use to analyze an actual sentence. Wikipedia offers a more thorough explanation:

A finite verb is a form of a verb that has a subject (expressed or implied) and can function as the root of an independent clause.... In many languages, finite verbs are the locus of grammatical information of gender, person, number, tense, aspect, mood, and/or voice. Finite verbs are distinguished from non-finite verbs, such as infinitives, participles, etc., which generally mark these grammatical categories to a lesser degree or not at all....

English is one of the many languages that only inflects finite verbs. However, inflection is not a defining trait, because some verb classes lack inflection for other reasons. The preterite-present verbs are one such class that inflects only for tense.

That class includes the English modal verbs, which have two relevant properties:

• They do not inflect, except insofar as some of them come in present–past (present–preterite) pairs. They do not add the ending -(e)s in the third-person singular....
• They are defective: they are not used as infinitives or participles..., nor as imperatives, nor ... as subjunctives.

Thus:

• Some modals do inflict for tense.
• Those that don't inflict do so for linguistic reasons, not grammatical reasons.
• Modal verbs are only used as finite verbs, as the root of the sentence.

Therefore, in the sentence “We could practice our dialogue,” could is a finite verb, functioning as the root of the sentence, that modifies the non-finite verb practice.

The definitions in Oxford Dictionaries Online describe some common traits of finite and non-finite verbs in English, but they overlook the key differences that you'd use to analyze an actual sentence. Wikipedia offers a more thorough explanation:

A finite verb is a form of a verb that has a subject (expressed or implied) and can function as the root of an independent clause.... In many languages, finite verbs are the locus of grammatical information of gender, person, number, tense, aspect, mood, and/or voice. Finite verbs are distinguished from non-finite verbs, such as infinitives, participles, etc., which generally mark these grammatical categories to a lesser degree or not at all....

English is one of the many languages that only inflects finite verbs. However, inflection is not a defining trait, because some verb classes lack inflection for other reasons. The preterite-present verbs are one such class that inflects only for tense.

That class includes the English modal verbs, which have two relevant properties:

• They do not inflect, except insofar as some of them come in present–past (present–preterite) pairs. They do not add the ending -(e)s in the third-person singular....
• They are defective: they are not used as infinitives or participles..., nor as imperatives, nor ... as subjunctives.

Thus:

• Some modals do inflect for tense.
• Those that don't inflect do so for linguistic reasons, not grammatical reasons.
• Modal verbs are only used as finite verbs, as the root of the sentence.

Therefore, in the sentence “We could practice our dialogue,” could is a finite verb, functioning as the root of the sentence, that modifies the non-finite verb practice.