I haven't yet deployed a big app with flask yet, but for my "playground" (Intranet App, very low load) I use Gunicorn (http://gunicorn.org/ ), which is extremely easy to set-up. For a deployment you would want to put nginx in front of it to serve static data.
If you just want do develop and test some things the server it comes with is absolutely enough and helps a lot with the debugging. Its as easy as typing "python myapp.py".
For deployment, it's also important to have something like nginx in front of Gunicorn to buffer requests from slow clients. Otherwise, this sort of thing can DoS your server pretty bad:
Skip it and go with uWSGI ;) Emperor mode is fantastic.
Say you have /srv/mysite/uwsgi.ini and /srv/myothersite/uwsgi.ini (uwsgi config files for two different sites) you can run uwsgi --emperor /srv/*/uwsgi.ini and bam, it'll launch processes for all your sites.
If you just want do develop and test some things the server it comes with is absolutely enough and helps a lot with the debugging. Its as easy as typing "python myapp.py".