Ping sweep for network:

nmap -sn -PE <IP ADDRESS OR RANGE>

Scan and show open ports:

nmap --open <IP ADDRESS OR RANGE>

Determine open services:

nmap -sV <IP ADDRESS>

Scan two common TCP ports, HTTP and HTTPS:

nmap -p 80,443 <IP ADDRESS OR RANGE>

Scan common UDP port, DNS:

nmap -sU -p 53 <IP ADDRESS OR RANGE>

Scan UDP and TCP together, be verbose on a single host and include optional skip ping:

nmap -v -Pn -SU -ST -p U:53,111,137,T:2125,80,139,8080 <IP ADDRESS>