you can use SDR (Species diversity and Richness) software, if you want a free software i offer PAST software, if you not familiar with R language i suggest you can use BiodiversityR package in R, and if you are, use Vegan package.
for more information read the file and use the scripts.
Indeces like Shannon-Weiner or Simpson can also be calculated in Excel. On youtube there are great tutorial videos for this.
For more complicated methods I thnk R is the best. It can be adjusted and tuned to your needs and requests of the task you are working on. Also - as it was written before - different packages are available in this environment.