Here are five basic commands every dog should learn:
Sit
Take a treat in hand. As you hold the treat, get your dog's attention. Raise the treat up in the air, causing their head to follow and their bottom to naturally go down. Once your dog has reached a seated position, say "Sit" and give them the treat and a little praise. Repeat over the course of a couple days. This will teach the dog to sit on command when situations arise and they need to be calm.
Come
While your dog is on a leash and collar, lean down and tell your dog to "Come" while pulling the leash toward you. Once the dog walks to you, give him/her a treat. Keep trying further and further distances until you feel confident the dog has mastered the command. Remove the leash and the collar in a safe and confined area and practice the command off the leash. Learning this command will keep your dog out of trouble.
Down
Hold a treat in your fist and put your fist to the dog's snout so they know you have it. As they sniff, move your hand down to the floor so their head follows, then move your hand across the floor to encourage your dog's body to follow by laying on the floor. After they are in the laying position, say the word "Down" and then give them retreat. Repeat the process until your dog has understood the command.
Stay
Teaching your dog to stay will first require they have mastered the sit command. Once they have, tell the dog to sit and then posture your hand in front of you with palm facing out towards the dog and say "Stay" firmly. Take a few steps back and if he/she stays, give a treat and some praise. Keep practicing moving farther and farther away each time.
Leave It
Put a treat inside your clenched fist and show your dog. Allow him/her to sniff, scratch, etc. at the hand with the treat until they stop. When they stop, say the words "Leave it," give some praise and reward them with the treat. Keep practicing this until your dog learns to not do anything with the treat in your hand upon you saying "Leave it."
Read more at dog obedience training.