The basic form is "traer", that's right.
TRAER means TO BRING
For example the Present is: yo traigo, tú traes, él trae, nosotros traemos, vosotros traéis, ellos traen.
The sentence "Bring us something, please" is using the imperative.
Imperativo: trae (tú), traiga (él, usted), traigamos (nosotros), traed (vosotros), traigan (ellos, ustedes)
So it could be translated as:
"Tráiganos algo, por favor" (Polite way, usted)
"Tráenos algo, por favor" (Informal way)
"Bring me something": "Tráeme algo" (with friends and used most of the time in Spain) or "Tráigame algo" (usted, very polite /formal)
"Bring her something": "Tráele algo" (informal) or "Tráigale algo" (polite)