What is the purpose of our life? In our short life what does Allah wants us to do and how do we know we are going in the right direction?
As for the first part of your question, please see my answer to the same question in this post: Purpose of the Worldly Life.
As for the second part of your question "how do we know we are going in the right direction", the following may be used as an indication that insha'Allah you are doing well:
- Being guarded from committing sins and mindful of your religious obligations, as you understand them.
- Observing the directives given in verses 22 to 38 of the Sura of al-Asraa
- Feeling pleasure from and enjoying worshiping God
- Feeling obliged to correct the false and help the truth
- When you are alone, being at least as good person as you normally are in the company of others
- Being so much interested in truth that leaves you open minded in correcting yourself when you find you have had a wrong understanding