I visited speakingan English speaking club yestuerday.

Generally, when we turn a <verb> <object> phrase into an adjective, we do so in the form <object> <verb>ing. Refer to words such as groundbreaking, skydiving, awe-inspiring, etc.
Also, don't forget your articles!

I met different people from different countryies.

I played the board game "Codenames" two times.

One may consider using "twice" here over "two times." What do you think flows better?

I didn'thad never played this game before.

had not/hadn't is also fine.
If you say didn't, it sounds like you had the opportunity before but chose not to, or like "before" is referring to some specific point in time when you did not play the game. Since we are talking about general experiences here, we need to use the "have not X" construction.

I don't drink any alcohol totaly.

You could also say something like "I never drink alcohol."
In English, you cannot use "totally" in the negative like this.

I met different people and they haved different jobs.

This may seem a bit counterintuitive, but in English, the tenses of descriptions in the context of talking about a larger event or occasion tend to follow the tense of the event itself, even if these people still have these jobs in the present.
Because you already said "I met different people" above, you may consider instead something like "The different people I met had different jobs." or even "The people there had many different jobs."

A doctor, a teacher.,

Why a period?

a student.,

a clerk, etc.

In English, a "clerk" can be many different things, so one may expect there to be a more specific description in this case (e.g. "bank clerk," "office clerk," etc.).
Also, most style guides of English consider it appropriate to include the Oxford comma (comma before the last item in a comma-delimited list).

Mostly, I could mostly explain what I wanted, but sometimesoccasionally, I didn't know how to explain.

Adverb position
Tense
The "how to explain" here is a bit awkward because one would expect an object (explain what?), but then there isn't really a good way to specify one without being repetitive.
I would just phrase it completely differently, like maybe "I could mostly explain what I wanted, but I occasionally had some difficulty."
On that note, I think occasionally fits the nuance here a bit better than sometimes; sometimes feels like you are describing a much wider reference point, whereas here, you're just talking about this one occasion.

I need add more words toto expand my vocabulary.

"I need <to> add more words..." is totally fine, but to "expand [one's] vocabulary" is a commonly used expression that could make this sentence sound more fluent.

I visited speakingan English conversation club yestuerday.

I met different people from different countryies.

I played a board game called "Codenames" two times.

I dihadn't played this game before.

I don't always drink alcohol totaly.

Mostly, I could explain what I wanted to, but sometimes I didn't know how to explain.

I need to add more words to my vocabulary.

I visited speakingan English speaking club yestuerday.

Or "An English Conversation club"

I met different people from different countryies.

I played the board game "Codenames" two times.

I love that game!

I didn'thad never played this game before.

I don't usually drink alcohol totaly.

If you don't drink much, then usually. If never, "I never drink alcohol."

I met different people and withey have different jobs.

or "various people"

A doctor, a teacher.,

a student.,

Mostly, I could explain what I wanted, but sometimes I didn't know how to explain.

I need to add more words to my vocabulary.