Welcome to Electronics Point!
Before we get into a long and involved discussion, please tell us about your electronics background and experience. Why do you want to build instead of buy?
If you want to be an electronics hobbyist, as most of us who respond to questions here in the Forum are, you need certain tools to "play" with. Among the most important of these is a decent digital multi-meter with at least three and a half digits resolution. Many of these are available with a capacitance measuring function, and all of them measure resistance. Finding an accurate inductance-measuring instrument is fairly easy and many of these use the same circuitry to also
measure capacitance.
I was recently gifted with a very nice combination inductance and capacitance measuring instrument that is commonly available for purchase on the Internet as a kit or fully assembled. Try this
Google results page for links to sources. And
here is a review of a typical DIY kit. When shopping around for LCR meters, know what range of inductance, capacitance, and resistance you want to measure and compare that against the specifications of whatever meter or DIY circuit you are considering buying or building.
The measuring procedure for resistance is quite simple: a constant-current source is applied across the unknown resistor and the resulting voltage across the resistor is linearly proportional to its resistance. Resistances from nearly zero to several meg-ohms can be measured with virtually any digital multi-meter.
The measuring procedure for reactive L and C generally uses an alternating current to measure the reactance of the component at a specific frequency. The reactance measurement is then converted (by a microprocessor) into inductance or capacitance. In multi-meters that provide a capacitance measuring function, a constant current is often applied to the unknown capacitor (as in resistance measurements) and the time required to charge the capacitor between two voltages is measured. This time is proportional to the capacitance.
The instrument that Steve linked to in post #2 is the most basic LCR measurement instrument. It uses a bridge circuit to compare an unknown LCR component value against a known precision LCR standard. Nice to have one of these around if you can afford it, especially if you are interested in metrology.