There are three main ways to turn an adjective into an adverb in Latin. In decreasing order of popularity:
- Use a special adverb-forming suffix: first/second adjectives get -ē, while third adjectives get -ter. This can be done freely to pretty much any adjective (famōsē, rubrē, calidē, velociter, prūdenter).
- Use the neuter accusative form. This is also quite well-attested, but less productive; it's where third comparative adverbs in -ius and (non-comparative) adverbs in -e come from (facilius, facile, multum).
- Use the neuter ablative form. This one was dying out by Classical times, mostly showing up in set phrases and fossilized expressions, but it's the ancestor of the extremely common -ē mentioned above (verō, falsō).
The first at least was still productive in Classical times; I'm not aware of any adjectives which couldn't be turned into adverbs in one way or another.