There are three main ways of multiplying your plants - budding and grafting, rooting cuttings and growing seeds.
Certain varieties seem to root readily from cuttings. Without extra base heat, I’ve succeeded with Meyer’s Lemon, Ponderosa Lemon, Bears’ Seedless Lime and some citrons. I’ve also seen Calamondin and Limequats for sale which appear to have been grown commercially from cuttings. I've recently been using a heated propagator, thermostatically controlled at around 27C (80F), and kept at 100% humidity. Most varieties root rapidly, but a few cuttings have succumbed to moulds and rot. No doubt with professional heating and misting equipment success would be even greater. From the point of view of UK pot-grown citrus one disadvantage in growing from rooted cuttings may be an increased danger of 'foot-rot' in damp conditions. Of course, the possible improvements in cold-hardiness, yield, fruit quality and soil-type adaptability provided by a rootstock will also be lost.

Citrus
seed must be sown fresh and germinates readily between 20C and 28C. However, it can take up to 20 years for seedlings to flower and produce fruit. They also tend to be thorny. Unusually for the plant world, some citrus varieties produce multiple seedlings from one seed – a phenomenem called ‘polyembriony’. If this happens, one seedling is the result of pollination and may eventually produce a completely new hybrid plant, the others are exact clones of the mother plant. Thus, citrus does often grow ‘true-to-type’ from seed. Reference books will tell you which varieties are polyembrionic.

Citrus seedlings can be used as rootstocks for budding/grafting named varieties. This can alter the fruit quality, disease resistance and tolerance to different growing conditions eg. soil-type and climate. Exact choice of rootstock is much discussed by commercial growers but for potted plants, where maximising fruit yield and quality is not an absolute priority, it is probably less important. Poncirus trifoliata is clearly the hardiest rootstock, but I find the vigorous growth of Rough Lemon and the Citranges an advantage.
Budding or grafting requires some expertise and available rootstocks and budwood for the 'scion' , the fruiting variety. There is an excellent description of the budding procedure from Texas Citrus; another at the Florida Gardener web-site, and one in French but with lots of photos at INRA, Corsica. There is also a useful agricultural student's course on citrus budding, with an East African slant, at http://instruct1.cit.cornell.edu/courses/hort400/4tutos/tbuddi1.html .
budding
Recent budding
PT seedlings
Poncirus trifoliata seedlings
PT cuttings
Poncirus trifoliata cuttings take forever to root outside!
cut Rough Lemon
Rough Lemon - Citrus Jambhiri. My plants originate from the rootstock used by the old Rivers Nursery. They have only recently started fruiting and so far have been seedless. Not much use for seedling rootstocks, so I am continuing to take cuttings which root fairly easily.
Updated 11 Dec 2003
Rough lemon