Your topic and actual question are really two things. Compound words are single words comprised of two roots (like "doghouse"). But "forest fire" is just a noun and a modifier. While "forest" looks like a noun, it's really acting no differently from an adjective. For a noun + modifier, this is a simple thing. The Romans mostly put nouns before adjectives (with some exceptions), whereas in English we put the modifier before the noun.
One thing you would not do though is put two nouns side by side. One would inevitably change either into a genitive or an adjective or some other modifying construction.
For something like forest fire, there would be a plethora of ways to say it:
- incendium in silvis (a fire in the forests) (noun + prepositional phrase)
- incendium silvae (a forest's fire) or ignis silvarum (forests' fire) (noun + genitive)
- incendium (quod) ortum/pervagatum in silva/silvis (a fire that broke out/spread in the forest(s)) (noun + participial phrase or relative clause)
I suppose technically you could do a calque on the English and end up with incendium silvestre, but that particular usage is unattested and would be stretching the definition of that adjective a bit. In this case, it doesn't work well.
One thing you have to keep in mind for all of these is that the fire is the main noun. "Forest" is the modifier; it's what modifies what type the noun is. So a forest fire is to be differentiated from a house fire or a pantry fire or a grease fire — all of them types of fire, and the word in front indicates that type. Similarly, a "brick house" is a house first that is made of bricks second. Fire/House is the noun in Latin, forest/brick is what modifies it.
Actual compound words are rarer. These are single words comprised of two roots. In English the only real difference is a lack of a space, but in Latin and Greek, there was a vowel that made pronunciation easier. They generally were either archaic and rarely generative (agricola) or else feel a bit ridiculous to say, and any new coinages were pretty much limited to poetry and were built on existing Latin models (though usually with an eye toward a Greek original). Mayer and Adams' Aspects of the Language of Latin Poetry has a lot to say on that topic. This is where we get words like ignifer (fire-bringing) and magnanimus (the Latin was typically magnus animus, but the Greek was the compounded μεγάθυμος).
From Cicero onward we see a greater acceptance of Greek borrowings (although they were present in the early poets, like Lucilius). Greek was much freer in compounding words, and honestly their compounds sound better to my ear, at least most of the time. It wasn't a complete free for all, but it was common enough that English has borrowed more compound words than single words. For "forest", you'll want to use hylo- as a prefix. With fire, it's unsurprisingly pyro-.
With these words in particular things get tricky - I know of no suffix with -pyr or -hyle and no Greek word meaning "forest fire." Typically, like Latin, the modifying word goes first, so we should end up with something like hylopyr, but does that ever look weird! It's much easier when talking about "pyromania" or "hylophagous instead. The latter might actually, work, though, and you could end up with a "hylophagous fire" - a forest-eating fire!