I've been in that situation frequently, having picked up guitar "knowledge" in fits & starts from a wide variety of people.

I can, I believe, improve on Richard Bridge's suggestion somewhat, because I was once told by a roomie who had a PhD in music (he played keyboards) that the melody note is likely to be the MIDDLE note in a suitable triad. So if the melody note at that point is F#, try playing a D behind it. Yes, other chords exist with F# in the middle, but you will have cut the number of options way down.

What I usually do now is experiment with the more common progressions in the key of the song, once I figure out what that key is or what key I want to play it in. There are a few "accidentals" which can be buggers to guess right, but most of your chords are going to be interrelated in a simple way.

(I don't know how much "theory" you're into or how you think of it, but if I Roman-number the notes of the scale of the key I'm in, songs are going to start building around I, IV and V, aka the tonic, sub-dominant and dominant, aka C, F and G, or E, A and B (Louie, Louie), or whatever. Patterns can be I-IV-I-V, or I-IV-V-I, etc.

A few do a mournful thing where they drop from I to VII. "Blue Diamond Mine," a real sad mountain thing, goes I-VII-I-V-I. That works for a few other songs too.

In both those cases, actually, instead of playing V as a straight major, you play its seventh, so it's really I-IV-I-V7.

You can also go from I to III, especially if a phrase almost repeats and you want to ramp up the second repetition. You could play the line "Five foot two, eyes of blue" all on I, but it sounds better as (I) Five foot two; (III) eyes of blue ....

You've also got very common four-chord progressions like

    Tonic to relative minor to sub-dominant to dominant 7th,
    which in C is C, Am, F, G7. (Everly Bros.; Dream, etc., etc.)

    Or it varies to C, Em, F, G7 (I Started a Joke, etc., etc.)

Finally, you've got "passing chords" to get from one principle chord to another. I-I-IV-IV might be changed to I-I7-IV-IVm or I-I7-IV-IVdim. I'm discovering that a lot of times if you have a change from I to V, you can make it I-II-V and it sounds closer to the melody and a whole lot more exciting. (Waitin' for a Train, e.g.)

Ignoring the fact that as an inveterate (invertebrate?) "trad" person I have probably given you examples you have never heard of [:)], I hope that helps. All this to say: stay in the key and try the middle note idea, & come back and tell us what works.

BTW, what's the song??

Best of luck,
Chicken Charlie