Rozumiem ten proces.

Rozumiem is the 1st person singular present tense form of the verb rozumieć (to understand).

So:

• rozumieć = to understand
• rozumiem = I understand

The ending -em tells you the subject is I, so Polish does not need a separate word for I here.

Polish usually omits subject pronouns when they are clear from the verb form.

So:

• Rozumiem ten proces. = I understand this process.
• Ja rozumiem ten proces. also means I understand this process, but ja is added only for emphasis, contrast, or clarity.

For example:

• Ja rozumiem, ale on nie rozumie. = I understand, but he doesn’t.

In a neutral sentence, leaving out ja is completely normal.

Before a masculine singular noun like proces, the usual demonstrative adjective meaning this is ten.

So:

• ten proces = this process

To can mean this/it, but it is not used the same way before every noun. For example:

• To jest proces. = This is a process.
• ten proces = this process

So in your sentence, ten is the correct form because it directly modifies the noun proces.

Very good question. In Polish, direct objects often go into the accusative case. However, for masculine inanimate singular nouns, the accusative is often the same as the nominative.

That is exactly what happens here:

• nominative: ten proces
• accusative: ten proces

So the object does function as an accusative object, but its form happens to look the same.

This is because proces is:

• masculine
• singular
• inanimate

If the noun were different, you might see a clearer change.

Proces is a masculine inanimate noun.

That matters because in Polish:

• adjectives and demonstratives must agree with the noun
• case endings depend on gender
• object forms can change differently depending on whether a noun is masculine animate, masculine inanimate, feminine, or neuter

Because proces is masculine singular, you get:

• ten proces = this process

If it were feminine, for example, the form of this would be different.

The normal, neutral order is:

• Rozumiem ten proces.

But Polish word order is more flexible than English word order. You can change it for emphasis.

For example:

• Rozumiem ten proces. = neutral
• Ten proces rozumiem. = This process, I understand / emphasizing this process
• Ja rozumiem ten proces. = emphasizing I

Even though the order can change, the standard version for a learner to use first is Rozumiem ten proces.

A rough English-friendly guide is:

• Rozumiem ≈ ro-ZOO-myem
• ten ≈ ten
• proces ≈ PRO-tses

More approximately in IPA:

• Rozumiem = [rɔˈzu.mjɛm]
• ten = [tɛn]
• proces = [ˈprɔ.t͡sɛs]

A few useful notes:

• Polish r is trilled or tapped
• z in rozumiem sounds like English z
• c in proces sounds like ts
• Polish stress is usually on the second-to-last syllable, so:
  • roZUmiem
  • PROces

It is the present tense, but like English I understand, it can describe:

• what is true right now
• a more general state

So Rozumiem ten proces can mean:

• I understand this process right now
• I understand this process in general

This is the normal verb to use for understand.

The infinitive is rozumieć (to understand).

There is also a related perfective verb:

• zrozumieć = to come to understand / to understand completely

This creates a useful contrast:

• Rozumiem. = I understand.
• Zrozumiem. = I will understand / I’ll come to understand

So in your sentence, rozumiem focuses on the current state of understanding, not the moment of reaching that understanding.

Usually, no—not if you mean I understand this process.

• rozumieć = to understand
• znać = to know / be familiar with

So:

• Rozumiem ten proces. = I understand this process.
• Znam ten proces. = more like I know this process / I’m familiar with this process

In many situations, those are different ideas. If you mean comprehension, rozumiem is the right choice.

It specifically means this process.

• ten = this
• proces = process

So:

• Rozumiem ten proces. = I understand this process.

If you just wanted the process in a general sense, Polish often uses the noun without an article, because Polish has no words for a/an/the.

So context decides whether a bare noun means a process, the process, or simply process in a broader sense.