Hearing the different sounds that make up words is one of the first steps in learning to read. This is called phonemic awareness. Phonemic awareness is all about hearing, so any activities to learn phonemic awareness will incorporate listening.
Before your child can isolate the specific sounds they hear in words, they can practice listening for sounds in every day life. Try making a sound and having your child repeat it. Then make two sounds together. When they get the hang of it, increase to a series of 3 sounds.
Sounds You Can Make
Objects that make interesting, distinctive sounds. Some examples follow:
banging on wall/table/lap
blowing
blowing a whistle
blowing nose
clapping
clicking with tongue
closing purse
coughing
crumpling paper
dropping (various things)
drumming with fingers
folding paper
hopping
Rhyming
Rhyming is a big part of phonemic awareness. Read rhyming books to your child. The works of Dr. Seuss are fantastic books with plenty of silly rhymes to catch your child's attention. You can pause at the end of a sentence to check for rhyming words. Ask your child to come up with another word that rhymes.
For example, In There's a Wocket in My Pocket (Seuss, 1974), initial sounds of everyday objects are substituted as a child talks about the strange creatures around the house, such as the "zamp in the lamp." (readingrockets.com)
You can also play a game, Rhyme or No Rhyme? Say two words and ask, do they rhyme? To turn the game around, have your child quiz you.