How to decide authorship order in this situation? My master's supervisor and I are working on a research project. He offers me the research equipment and the basic ideas. He also writes the paper. I am in charge of coding and conducting all the experiments and analyzing the results. Sometimes I will discuss with him about my ideas but he is the one who decides to use them or not. 

Should I be listed as the first author or not?
If you are performing most of the work responsible for conducting the research (designing and conducting experiments, handling the results, etc., just as you say) then you should be the first author. This makes it pretty easy to handle the problem if the only authors on the paper are you and your supervisor. If this is the case, and there is a debate about authorship, you may even elect to list yourselves as co-authors who made equal contributions, though you will still likely be the first author. 

There's been a fair amount of published discussion about this subject, as with this 2007 paper by Tscharntke et al. in PLoS Biology.