How do I know whether to use strong, weak, or mixed declension?

It depends on the word preceding the adjective:

Strong: No article / "article-like" word that doesn't show strong endings (e.g., viel, wenig, etwas, nichts, mehr, mehrere, einige, manche, andere, allerlei).

Weak: Definite articles (der, die, das), demonstrative pronouns (dieser, jener, solcher), alle, beide, jeder.

Mixed: Indefinite articles (ein, eine, ein), possessive pronouns (mein, dein, sein, ihr, unser, euer, Ihr), kein.