Here you're using a graduated cylinder to measure the volume of water. Since you're using water as a chemical in this experiment, use the deionized water from the gray spigots. You get the mass of the water by weighing the cylinder before and after you add the water. Make sure you record the mass and volume to the correct number of significant figures. On the balance, it's what you read. On the cylinder, check the markings, then go one decimal place beyond what is marked. The density is the mass divided by the volume.
Table 2.1 (page 11) shows the "true" densities of pure water at various temperatures. The formula for calculating the "estimated precision of a set of measurements is on page 1 of your Lab Manual. The formula for "systematic error" is on page 2.
This part is fun. You get an unknown solid (a metal), and weigh it, then you put in a graduated cylinder, which is partially filled with water, to determine its volume. You don't need to use deionized water on this one, since water is not the chemical of interest (and it does not react with the metals). Calculate the volume of the metal by difference, then calculate the density and compare it to list in Table 2.3 on page 12.
As always, you must write your own report and do your own calculations for each lab report, even if you're working in a group or with a partner. Sometimes, you will advised to work in groups of 2-6 students (the number will vary depending on the activity), and data will be shared among group members. If you've been instructed to work individually (no partners or groups), then copying of data is not allowed. Copying calculations and answers to questions is NEVER allowed. You must do your own work. Discussing it is okay, but if you copy without thinking, you're cheating. Try at least to reword an answer, or set up a problem in your own way, than to copy directly from someone else.