Titration is a process designed to find out the composition of solutions. For example, if a solution is known to be a solution of hydrochloric acid in water, what percent of the solution is hydrochloric acid? This test can be accomplished by putting a sample of the solution in a graduated cylinder (so you know how much you are starting with) and then adding--a drop at a time--a base of known concentration. At the exact point when the solution changes color, look at the graduated cylinder and see how much of the base was added. From this experiment you get all the information necessary to calculate the strength of the beginning solution.
The density of a substance is equal to its mass divided by its volume. Density is an intrinsic property of a material. It you are looking at something that looks like gold, but its density is not that of gold, then the thing is not pure gold. To find the density of a liquid, weigh it and then pour it into a graduated cylinder. Divide mass by volume to get density. To find the density of a solid object, weigh it and then fill a graduated cylinder with enough water to reach the top half. Note the volume of water in milliliters. Put the object in the water and note the new level. The volume of the object is the new water level minus the old water level. Compute the density of the object by dividing the mass by the volume.
Graduated cylinders are used in several gas experiments, but these almost always involve inverting the cylinder (so the gas does not escape). Therefore, you must remember to read the scale upside down. The simplest such experiment is using a graduated cylinder as a barometer. Fill a sink or large tub with water and submerge a graduated cylinder so that it has no air in it. Carefully turn the cylinder up without letting any air in--the cylinder should be tall enough so that it now sticks out of the water. The top of the inverted cylinder should now have a small vacuum, because the ambient air pressure in the room will only support a column of water of a height less than the height of the cylinder. Reading the water level will tell you the air pressure in the room. In experiments that generate gases, use a graduated cylinder inverted in water as in the barometer as a collector. Run a tube from the gas generating apparatus into the inverted cylinder to trap the gas and see how much was generated.