There are now many ways to install plumbing without solder but you should never install PVC for water supply lines inside a house. PVC for water supply is not allowed inside the home under almost every code that I know of and is never allowed for hot water. There are other materials that may be used such as CPVC, and PEX. There are also connectors called SharkBites which copper, CPVC, and PEX many be pushed into making a connection. 
You should always check with your local building inspection officials to find out if the materials you are planning on using are allowed in your situation and if you are allowed to do the work yourself. There is some special glue which are currently being marketed that the makers claim will glue copper fittings and tube together but I would not recommend their use as there are many better methods which can be used and I also say again you should ask a local building inspection official before using any glue on copper.
PEX Tubing is an excellent material choice for plumbing without soldering. PEX tubing is made with a cross-linked polyethylene that is very flexible and allows you to run your water supply lines almost like wire. Some tools are required to install PEX. There are 2 basic assembly methods used. The first is the expansion method where a collar is placed over the tube then an Expansion Tool is inserted into the tube, which expands the tube allowing a connector to be placed in the tube, which then contracts back to its original size gripping the connector.
The second is the crimp method where either a copper ring or a stainless steel crimp (SSC) ring is placed around the tube then the connector is placed into the tube then the crimp ring is crimped securing the tube to the connector much like a hose is secured with a hose clamp. The copper ring tool crimps around the outside of the crimp ring then proper crimping is verified with a go/no-go gage, because the tool goes around the outside of the ring different jaws are needed for different sizes of tubing. The stainless steel (SSC) has an ear on one side of the ring where the tool grabs the ear and squeezes it together making the crimp ring tighten then releases once the crimp is complete.
The same tool is used for all the ring sizes so only one tool is needed. If you used a SharkBite to make the initial connection to the existing supply you could plumb almost a whole house without soldering. PEX is easily cut using a PEX cutting tool where you just squeeze the handles and a knife cuts through the tube.
CPVC tubing is a fairly rigid tube that is used very much like copper with a wide variety of connectors and elbows used. The CPVC connectors are bonded to the CPVC tube by using CPVC Cement. When connecting CPVC a metal threaded connection it is advisable to use a special transition connector that has a brass threaded portion molded into the CPVC connector. Plastic to metal connections should be avoided, as they will leak especially on the hot supply lines. For stop valves at fixtures compression connections can be used and there are also chrome plated brass valves that have a CPVC insert, which can be glued on. Another possibility is using valves with have a push on connection similar to the SharkBite. CPVC is easily cut using a small ratcheting cutter, which sends a knife through the CPVC easily cutting the tube.
Both PEX and CPVC allow plumbing supply lines to be installed without using any soldering of pipes. Research the materials you select to see the materials and methods used and available so that you can do the work properly and make sure the material you select is allowed where you live in your application.
