Answer:
A terminological note: nouns, adjectives and pronouns have declensions; verbs have conjugations.
If you have the infinitive (second principal part) and length markings on your vowels, the task is easy:
1st conjugation: infinitive ends in -āre (passive/deponent -ārī)
2nd conjugation: infinitive ends in -ēre (passive/deponent -ērī)
3rd conjugation: infinitive ends in -ere (passive/deponent -ī)
4th conjugation: infinitive ends in -īre (passive/deponent -īrī)
If you have the infinitive but no length markings, you can tell the 2nd and 3rd conjugations apart by looking at the first-person singular indicative (the first principal part). If this ends in -eo, it's a 2nd-declension verb; if it ends in -io, (e.g., capio) or just -o (e.g., cano) it's 3rd.
If you don't have the infinitive, knowing one or more forms from the present indicative can help:
1st conjugation: first person singular ends in -ō, third singular in -at
2nd conjugation: first person singular ends in -eō, third singular in -et
3rd conjugation: first person singular ends in -ō or -iō, third singular in -it
4th conjugation: first person singular ends in -iō, third singular in -it
In the absence of the infinitive, -iō verbs of the 3rd conjugation can be hard to tell from 4th-conjugation verbs. Having vowel markings can help; for example, 4th-declension venīmus "we come" (long ī, accent on the second syllable) versus 3rd-declension capimus "we take" (short i, accent on the first syllable). The imperatives also differ: 4th-declension venī "come!" versus 3rd-declension cape "take!"