How do you say the verb run in a sentence as a noun?
The part of speech you are looking for is known as a gerund. Usually, the verb is conjugated with the form that terminates in "—ing" when it's used in a sentence. For example, in the sentence,
"running" is not being used as a verb, because it is not an action that Alex is (necessarily) performing or the state that Alex is in, but rather a noun, used to describe a field of knowledge or a general class of activities that involve the verb.
In the sentence
run is used as a noun meaning a race in which you run.
You can use it in the sense of "a continuous spell of a particular situation or condition":
or to describe the scoring of a point in baseball:
or in the sense of "a widespread and sudden or continuous demand for [something]"
or as "a track made or regularly used by a particular animal"
or in the meaning of a "journey accomplished or route taken by a vehicle, aircraft, or boat, esp. on a regular"
There are others, but you get the idea.
The other answers here explain well the situation with run, but in general, verbs cannot be used as nouns.
Many verbs do have noun senses—that is, when used as a noun, the word has a set meaning related to the verb. However, the nature of the relationship between the verb sense and the noun sense is not necessarily predictable. In some cases, the noun use of a verb is an instance of that verb being acted—e.g. run, drop, bounce. In other cases, the noun use is the result of the verb—e.g. mash, mix, spit. In most cases, however, you form a noun from a verb by adding a nominal suffix, such as these:
Since you cannot predict which suffix to use, or whether to use a suffix at all, you have to memorize each case.
How does this relate to the original question? The questioner asked “how do you say the verb run in a sentence as a noun”. The answer is “you don’t”. You can use the word run as a noun—because it has meaning as a noun—but the verb run can only be used as a verb.
There is one further point: that of the gerund-participle inflection -ing, which can be added to most any verb and used in noun position. The gerund-participle running can be used as a noun—e.g. “running is not my idea of a good time”.