In order to do this yourself, the tools needed are...
Tuck Pointing Trowels - 1/4", 3/8" and possibly 1/2"
Brick Jointer - 1/2" x 3\8" or 5/8" x 3/4" (they are double sided, each side has it's own size)
Brick Trowel - 5-1/2" is the easiest to work with
Cold Steel Chisel - 1/4"
Lump Hammer - 3lb
Grinder w/ a 4-1/2" masonry wheel (diamond blade, stay away from those black carborundum blades)
Shop Vac - small 5 gal is fine
Blue Painters Tape - place on the bricks to prevent the new mortar from staining the edges.
Safety Glasses
Knee Pads - gel filled are the best or one of those soft blue colored kneeling pads found in the garden section of Lowes
Small Mortar Tub - or something to mix the mortar in where it's easy to get it out
Mortar - premixed is fine (sand & mortar, not premixed as in wet). Number of bags will be determined by the size of the area being worked on. I like to use Type S (not Type N).
Start by using the chisel and lump hammer to remove the existing mortar. Never use a hardened steel hammer (lump hammer is best) on a chisel; you'll ruin the hammer & it'll bounce off the chisel possibly causing injury. Aim away from the pool to keep the chips in of the water to a minimum. If you find this tedious, use the grinder on the joints. Be careful using the grinder, the torque will inadvertently twist it in your hands and you may damage the brick. If using the grinder, wear a dust mask. After a section is done, clean out every joint with the shop vac. Mix the mortar to a consistency where it will hold together (not crumble), but not too wet where it's messy. Remember, the brick will draw the water out of the mortar like a sponge, this is what causes the staining. Mix small amounts at a time, never more than you'll think you'll use in a short time. If the mortar starts to get hard, it is NOT recommended to add more water. Make a new batch.
Using the 5-1/2" brick trowel scoop out a small portion using the edge of the trowel (do not scoop it out like a shovel). Carefully use the tuck pointing trowel to gently push the mortar off the trowel into the joint. Once the joint is almost filled, use the tuck pointer to push it in there real good. Then repeat the first step to "top off" the joint. Let the joint sit a while and then pass the brick jointer over the joint. This creates the smooth concave joint. If the joint is too "shiny" after using the jointer, lightly pass a clean dry paint brush over the joint, this will dull the shine a bit. Clean off the edges & remove the tape. Then repeat this step another 500 times or however many joints there are.