What i have been doing today

I have been went running. Then, I have driven drove to the airport and going went shopping at to a new shopping center in the city closer closest to mine. 

You would might ask if I don't work; yes I do, but I am a teacher, therefore i have two months of holidays. Nice, isn't it? 
After lunch I have had my typical Spanish siesta for half an hour; it was too much hot. and The last thing i have done did is was taking take an i talki class with a good teacher.

Notes: Hi Rosa, nice job! Keep working on the use of past simple (i.e. I drove to the airport) vs past perfect (i.e. I had driven to the airport). I believe past perfect is generally used to talk about something that happened before another action in the past. For example, you could say, "I had driven to the airport, and afterwards decided to go shopping." In this example,  the drive to the airport happened before the action of going shopping. This is contrasted with the present perfect - which you used correctly - an action/situation that started in the past and continues into the present (i.e. "Today has been a busy day for me".) Thanks for sharing!

*I would choose a different word here, such as: if you want to "participate in" outdoor sports

** I would rephrase this to something like: "you should wake up early to avoid fainting from the heat"

What i have been doing today

You might ask if I don't work. Yes I do, but I am a teacher, therefore i have two month holidays. Nice, isn't it?.
After lunch I have had my typial Spanish siesta for half an hour. too much hot, and the last thing i have done is taking a i talki class with a good teacher.

You are able to form sentences using these various tenses very well, but I'm not sure that you are using them correctly in terms of meaning. I highlighted one sentence in particular, this sentence looks to me as if it should be written in past simple. "I went running, then I drove to the airport and went shopping...".

I can see you are trying to use your English, and I praise you for doing that, but I suggest you revise the uses of the perfect aspect. 

It's not a problem to say "I have been running today" because of course today is an unfinished period of time, but when you follow this sentence with "then", you should change to past simple.

Why? Well, I think you should ask your teacher to explain in more detail because they have more time than I do ;) But in general, I would recommend using perfect aspect to talk about the relationship in time between the events you're speaking about.

I hope this helps! I will of course explain anything I've said that you don't quite understand!