Take a look at the date command. You can customize the format by which the date is displayed and embed it in shell commands using command substitution
mkdir $(date +%Y%m%d-%H%M)_my_dir
Take in mind that the format yyyymmdd is more suitable for file names, since they will be sorted in time order when displayed by the ls command. Also take a look at the -d option of date, to retrieve a date other than today.