Today, I waoke up early, specifically at 6:40 am.

I went out from my bed and I walked across the living room to got the refrigerator.

I opened the refridge and I took a someout water and 2two fruits, because at thisat moment. I decided to prepare a juice for my son.

After theI prepare me the juice, I went to the bathroom and I took a shower with boiled water, it. I was very relaxed.

I got dressed, specifically, I put on a Jean, my nike shoes and a T-shirt.

I gottook the bus at 7:30am and the bus traveled fast, so I arrived to my office at 7:50.

Todays'his morning before work

If you're talking about the morning of today, you can just use "this morning" instead. Think of it as being "this day's morning."

Today, I waoke up early, specifically at 6:40 am.

Since you're talking about the past, you need to use the past tense, "woke."

I wengot out ofrom my bed and I walked across the living room to get tot the refrigerator.

We don't use "went" for getting out of bed, as weird as it may seem. The bed is already implied to be your own (at least in this type of phrase), so you don't need to specify that it's your bed. Since you already established that you're the one doing things, you don't need to add "I" again after "and."

I opened the refridge and I took agot some water and 2 fruits, because at this moment I decided to prepare aI wanted to make juice for my son.

"Refri" is not a word, but if you wanted to use something shorter than "refrigerator," you should use "fridge." In fact, I almost only use "fridge." "Because at this moment" is really odd to say, not only because of the tense, but because it's just unnecessary to add. Instead, you can just say "wanted." I'm assuming you wanted to make juice for your son in this sentence. "Prepare a juice" wouldn't be incorrect if you were grabbing something like a juice box for your son to drink in a while, but it's odd if you mean to make it.

After the preparI made the juice, I went to the bathroom and I took a shower with boiled water, inice, hot shower. It was very relaxeding.

I would hope that you weren't taking a shower with boiling water, because your skin would be burned! Instead, you can just use "hot" since it's a pretty general way to describe water at a high temperature. This isn't necessary, but I added "nice" before "hot shower" because it emphasizes how relaxing the shower was.

At 7.15 am.

It's weird if this is its own sentence.

At 7:15am, I got dressed, specifically. I put on a Jpair jeans, my nNike shoes, and a Polo-Ralph T-shirt.

It makes more sense to add "7:15" at the beginning of the sentence, so I did that. Despite the sentence being short, it's okay to end it after "dressed."
"Jeans" is a little weird since it's basically already pluralized, even when you're talking about one. If you want to specify, you can say "a pair of jeans," but you can also just say, "I put on jeans."
"Nike" is a brand, so you can capitalize it.
Lastly, I combined your next sentence with this one by already saying what type of T-shirt you were wearing.

The T-shirt is kind of Polo-Ralph.

You can combine this idea with the previous sentence.

I got on the bus at 7:30am, and since the bus traveledwas fast, so I arrived to my office at 7:50.

If you don't add "on," it seems like you're saying that you bought a bus that you wanted, or something like that. Since you were connecting the sentences, I added "since" in place of "so."

It was a great trip from my homThe trip was nice, and the weather was very pleaseant.

You don't have to say that the trip was from home, as it's not necessary information. Instead, you can just say that the trip was nice. For the second part of the sentence, just pay attention to spelling.