Please help me!

Hi!  My suggested corrections are shown in < >.  My comments are shown in [ ].

Tet holiday was out of from today.  <Today is the last day of Tet.>

I will start with new targets and my efforts. <As of today, I will start working on my new goals.>

I set them the end of last year. [you don't need this line since you are talking about your NEW goals]

This year, I will try to spend time for physical exercise. <...spend more time doing physical exercise>

I get older. My health become worsen. <As I get older, my health becomes worse (worsens).>

Having the good health, I can work hard, earn more maney, enjoy more. <Having/Enjoying good health, I can,,,and enjoy life more>

 
Today my internet was suddenly trouble. <... my Internet broke down>

I called to the internet center. Luckily, they helped me quickly. <I called the Internet Center and luckily, they helped me quickly.>

If none, I wouldn't have had the internet connection to chat and write in my diary. <Otherwise, I wouldn't have had the internet connection to chat ....>

According to buddhism, from after the 4th day of the New Year, my ancestors aren't in my home. <According to Buddhism, after the 4th day of the New Year, the ancestors aren't at home any longer.>

As a result, we no longer offer many bunches of incense on my altar. <As a result, we no longer burn insence in our family altars>

[Your three lines about your Internet connection breaking down are a little off since you are talking about TET... you may conclude your entry with them, but they are still a bit out of place!]

Good luck with your writing!