3D printer are precision machines. There are many things that must go right in order to make successful prints. The machine must "know" how much filament is being extruded and must be calibrated to travel proper distances in order for the correct amount of filament to be extruded in to the part.
Most manufacturers ship machines with generic calibration settings. Due to variations in the manufacturing process these calibrations may or may not allow you to print on your printer out of the box.
The most important things to calibrate on a new machines are:
E-Steps - E-Steps allow the machine to know how many mm of filament it extrudes every full rotation of the extruder motor. Typically, this is done by marking the filament, extruding 100mm of filament through the extruder, and then measuring how much filament was actually extruded. The process to calibrate the E-Steps will vary from machine to machine but it generally involves knowing the current E-Step value, knowing how much filament you told the machine to extrude, and how many mm of filament was actually extruded. Using these three values you can calculate a new E-Step value.
Flow - E-Steps tell the machine how many mm of filament it is extruding, but due to variances in density from filament manufacturer to manufacturer (and sometimes even spool to spool) the amount of plastic actually extruded can be drastically different. By performing a flow calibration, combined with the E-Step calibration you can insure your printer is extruding the correct amount of plastic. Flow calibration is typically done by printing a small 5 sided box with walls the thickness of your nozzle. Once printed, measure the thickness of the walls and if it's not the thickness of the model adjust the "Flow Percentage" in your slicer program to account for the variance. This is typically a trial and error method.
Bed Leveling - For optical performance your bed must be "level". "Level", though, isn't really the correct word. "Square to the nozzle" is more accurate. Unless your machine, mechanically, is perfectly level and perfectly square a "level" bed isn't necessary and instead the bed should be square to the nozzle so that the distance between the nozzle and the bed is consistent across the entire bed. Most modern machines have an auto level function but it's still beneficial to get the bed as level as possible before performing the auto level function. If your bed has adjustment screws it's best to perform the leveling directly above each adjustment knob. One way to do this is to use a piece of printer paper and place it between the nozzle and the bed. Typically it is best to start with the bed adjustment screws set so the bed is almost as low as it can go (and thus loading the springs). Move the hot end above the first bed height adjustment screw and then lower it down until the paper is tight and you can feel resistance as you move the paper back and forth. Move to the next position and perform the same test and adjustment with the paper. Keep moving from point to point until all points have similar resistance on the paper. Once the bed is square to the nozzle remember to set your Z offset!
Z-Offset - The Z-Offset sets the distance between the nozzle and the bed. The Z-Offset should be adjusted so that the first layer of filament is "squished" but not completely flat. If the Z-Offset is too low the first layer typically will come out wavy due to the filament squeezing out and not laying down at a consistent height. If the Z-Offset is too high there won't be good bed adhesion and your prints won't stick to the bed. If prints are difficult to remove from the bed after the bed has cooled down increasing your Z-Offset slightly can help this.
X/Y/Z - If you tell your printer to print a 50mm cube and it comes out bigger or smaller than 50mm you are not extruding the proper amount of plastic (and also making inaccurate parts). For Delta styled printers, since they use all three axis to determine X/Y/Z position if your X and/or Y are off your Z will be impacted as well. Typically to calibrate X/Y/Z on Cartesian machines you print a calibration cube and measure it using a quality pair of calipers. This data is used to calculate the proper values that need to be inputted in to the printer and saved. To calibrate X/Y/Z on Deltas you typically will either do a Delta Calibration or adjust your Tower Angles (there are programs available to calculate the proper tower angel based on measurements). It is imperative that E-Steps and Flow have both been calibrated before doing an X/Y/Z calibration. If you are overextruding or underextruding these errors will impact your X/Y/Z calibration.
While there are other things that can be calibrated these are the "must dos" before you start running the printer. A properly calibrated printer will perform much better and much more consistently and hopefully allow you to avoid many hours of frustration trying to figure out why your prints are failing!