Clean the brick patio with a pressure washer. Point the nozzle so it cleans along each mortar line on the patio, as well as cleaning the bricks themselves. Power washing should remove the loose mortar and give you an idea of what you need to replace.
Match the sand used in the brick mortar with new sand. It may be a challenge to find the exact same color sand, but try to find sand that's in the same color range to avoid making the repairs look too obvious.
Mix one part sand with one part Portland cement. Add enough water to make the mixture the consistency of thick cake icing.
Set the nozzle in place inside a grout bag. Use a hand trowel to add the mortar mixture to the bag. Fill the bag about one-half full.
Spray water over the joints in the brick patio with a spray bottle. Do not saturate the joints, just dampen them.
Twist the top of the bag so the mortar flows toward the tip. Squeeze mortar between the rows of damp bricks to make the patio repair. Allow the mortar to top off each crack by about 1/4 inch.
Scrape off the grout above the patio floor when the mortar changes from shiny to dull colored. You should be able to press the mortar with your thumb and not have mortar stick to the thumb. Take care not to get mortar on the bricks. If you don't wait until the mortar dries sufficiently, it's likely to smear onto the bricks. If that happens, wait until the mortar dries, then brush it off with a stiff-bristle brush.
Dampen the mortar with the spray bottle. Keep it damp for three days as it cures. Depending on weather conditions, you may need to cover it with plastic sheeting to keep it from drying too quickly.