Learn Hardcore Arabic (Levantine): الاطار اسود.

The more standard spelling is الإطار أسود.
The ṭ in إطار is an emphatic t.
In some Levantine accents, أسود may sound a bit closer to iswed / iswid, but aswad is a good form for learners to recognize and say.

Why is there no word for is in this sentence?

Because Arabic often makes simple present-tense sentences without a verb to be.

So الإطار أسود literally looks like the frame black, but it means the frame is black.

This is very normal in both Standard Arabic and Levantine. If you want past or future, then Arabic uses other forms, but in the present tense, no separate is is needed here.

Why does the color word come after the noun?

In Arabic, descriptive words normally come after the noun they describe.

So Arabic says:

الإطار الأسود = the black frame

And in a sentence like:

الإطار أسود = the frame is black

the noun still comes first, and the description follows it. This is the normal Arabic word order.