Okay, a Dell and a small form factor to boot. What this means is that the build will only accept low profile cards. Also, the PSU is a non-standard size/shape so aftermarket replacement is out and you are stuck with a 235W PSU which is not much.
http://www.stuartconnections.com/3473-large/Dell-Optiplex-380-SFF-Small-Form-Factor-235-Watt-Power-Supply-RWFHH.jpg
Non-standard size/shape mobo so aftermarket replacement is out there too.
http://www.stuartconnections.com/383-794-thickbox/Dell-Optiplex-380-Desktop-SFF-Main-System-Mother-Board.jpg
https://en.wikipedia.org/wiki/Computer_form_factor
https://www.amazon.ca/Genuine-Dell-Optiplex-Motherboard-0HN7XN/dp/B00OI4UFTU
Only two RAM sockets which take DDR3L ram @ 1.35V. Good news here is that Crucial and the Dell forums are saying that contrary to the Dell tech doc it will support 2 X 4GB sticks.
http://www.crucial.com/usa/en/compatible-upgrade-for/Dell/optiplex-380-small-form-factor
http://en.community.dell.com/support-forums/desktop/f/3514/t/19609274
Last, not sure which CPU you have. If you don't know, run this program and it will tell you.
http://www.cpuid.com/softwares/cpu-z.html
Honestly, upgrading here is a bit of a mess. I would be very leery of replacing components with significantly higher wattage items. The graphics cards that Dell listed were only 19W cards, not much that can be had here. If you want to keep the 19W, best card would be a low profile GT 720. I could only find one, here it is.
https://pcpartpicker.com/product/9dNp99/pny-video-card-vcggt7201d3lxpb
If you were willing to try a 30W card, then an R7 240 is the best card you can install. I would go with the XFX card.
https://pcpartpicker.com/products/compare/XyJwrH,mmyFf7,7RQypg/
So to sum up, increase ram to 8GB and get an R7 240. Once you provide the current CPU we can consider upgrading that.
http://www.crucial.com/usa/en/optiplex-380-small-form-factor/CT8961419
https://pcpartpicker.com/product/7RQypg/xfx-video-card-r7240aclf2