I have saved several seeds from some small lemons and decided to try growing one or two. Here's how its done:

Get your seed from grapefruit/oranges/lemons/limes whatever it is you wish to grow and soak in water overnight.
Grapefruit is easiest, followed by oranges and then lemons.

Fill small pots with moistened potting soil. With your finger or pencil, make holes about 1" (2.5cm) deep in soil, drop seed into each and gently firm soil over them.

Water well, cover pots with clear plastic bags/empty 2L plastic pop bottle and set in warm bright spot. Avoid direct sun. When seeds germinate, take cap off top or open bags for a few hours a day to acclimate.

After 3 or 4 days remove cover. Indoors citrus plants need lots of sun, with temps around 21deg C, generous humidity (especially in winter) and regular feeding and watering.

High Temperature:
Actual: 10°C cloudy windy rain 2.3mm WInd NW28m/h P.O.P.40%
Average: 18°C
Record: 27°C in 1952

Low Temperature:
Actual: 3°C cloudy Wind NNW25km/h P.O.P.50%
Average: 7°C
Record: -1°C in 1942