How do you derive the adjectival form of an irregular verb such as "read"?

Nothing obviously, you can't really say "readed data" - perhaps with more of the context we can come up with something better.

English isn't always as clear as languages that can do things with verb endings - that's why technical phrases can sound clumsy.

The difference here comes in pronunciation, you would still use 'read' but speak is such as red or reed depending on the circumstance. For instance:

• I can reed.
• I red it.

Though, you could alter the sentence to replace 'read' with a couple of things, as per @Martin's comment 'entered' or 'loaded' could be used:

We do something with the loaded data.

We do something with the entered data.

We do something with the provided data.

Or it could be shortened, but this is depending on context:

We process the input.

here's a list of about 370 irregular verbs and from what you're asking here's some adjectives:

broken vase - from the infinitive "break"

burnt toast - from the infinitve "burn"

frostbitten fingers - from the infinitive "frostbite"

lip-read movie - from the infinitive "lip-read"

typewritten manuscript - from the infinitive "typewrite"

an so on and so forth, hope that helps! :)

I think that technically "read data" is correct, but it sounds awkward (and appears even more awkward). To make it sound less awkward (without resorting to a different verb) you can add an adverb or change it into a phrasal verb:

• the data read in
• the recently read data
• frequently read data

I think that those are fine.

I'm confused by fact that this verb irregular and is spelled the same in 1-3 forms.

Exactly. Your readers will be confused too, if you write something like “examine the read data”.

Grammatically, the read data is fine. Practically, it is a confusing mess. Treat it as you would treat code that's technically correct but confusing: rewrite it.

For your amusement: Some other past participles that are exactly identical to the present tense are bet, burst, cut, hit, hurt, let, put, run, set, shut, and split. Some of these can be used before a noun (some burst pipes, the hurt children), but most aren’t normally used that way in practice (the hit batter charged the mound would be strange). Read is not alone, though it is especially bothersome for programmers.

Workarounds: An adjective or past participle with complements of its own can go after a noun: the people hurt in the blast, the amount bet on the first race, batters hit by wild pitches, the data read from the socket, the data read so far.

However, it is probably best to just drop the confusing word read and say the data from the socket or all the input so far or the data in 'x' where x is a variable name.