There are three ways
1) This runs the GUI editor for the user environment variables. It does exactly what the OP wanted to do and does not prompt for administrative credentials.
rundll32.exe sysdm.cpl,EditEnvironmentVariables
(bonus: This works on Windows Vista to Windows 10 for desktops and Windows Server 2008 through Server 2016. It does not work on Windows NT, 2000, XP, and 2003. However, on the older systems you can use sysdm.cpl without the ",EditEnvironmentVariables" parameter and then navigate to the Advanced tab and then Environment Variables button.)
2) Use the SETX command from the command prompt. This is like the set command but updates the environment that's stored in the registry. Unfortunately, SETX is not as easy to use as the built in SET command. There's no way to list the variables for example. Thus it's impossible to do something such as appending a folder to the user's PATH variable. While SET will display the variables you don't know which ones are user vs. system variables and the PATH that's shown is a combination of both.
3) Use regedit and navigate to HKEY_CURRENT_USER\Environment
Keep in mind that changes to the user's environment does not immediately propagate to all processes currently running for that user. You can see this in a command prompt where your changes will not be visible if you use SET. For example
rem Add a user environment variable named stackoverflow that's set to "test"
setx stackoverflow test
set st
This should show all variables whose names start with the letters "st". If there are none then it displays "Environment variable st not defined".
Exit the command prompt and start another. Try set st again
and you'll see
stackoverflow=test
To delete the stackoverflow variable use
setx stackoverflow ""
It will respond with "SUCCESS: Specified value was saved." which looks strange given you want to delete the variable. However, if you start a new command prompt then set st will show that there are no variables starting with the letters "st"
(correction - I discovered that setx stackoverflow "" did not delete the variable. It's in the registry as an empty string. The SET command though interprets it as though there is no variable. if not defined stackoverflow echo Not defined says it's not defined.)