well, the stabilized varietes are what we call inbred lines and they are homozygous, which means the chromosomes of each chromosome pairs are identical (or quite, maybe some new varieties still have some genetic variations which aren't seen on the breeding goals).
these kind of varietes breed true when self pollinated for all traits (and they are the basis of commercial F1 hybrids).
so basically, when you cross two stabilized varietes, you're creating a F1 hybrid, and if the parents are well stabilized, all the plants from this cross will be gentically identical.
then you want to stabilize the cross to make it breed true for what you want (keep in mind you may not be able get exactly what you want, as some traits are linked on same chromosomes).
(note that you could just want to create a F1 hybrid variety and you'll be able to make some seeds again if you keep the parents by self pollination)
the main problem is that involves to grow a lot of plants if you want to maximize the chances to get the wanted genes combinations.
it involves another thing for the combinations, luck ^^
you can still try to make a new stabilized variety with few plant number, but you'll rely more on luck, and you may have to choose something a little different that what you would have wanted, but it's still worth a try for fun and you may get something good anyway, supposing you're crossing two good varieties
the way to stabilize a cross is to grow a few of the F1s, but normally they should be identical (or quite, there's always some differences in genetic expression with environmental differences), self pollinate them, you'll get F2 seeds
the F2 generation is the one that will show the most different combinations of genes, and so it should be better to grow as many plants as you can
sow the F2 seeds (preferably from the best F1 plant) and self pollinate them, you'll get F3 seeds
that's where the job begins to be funny, as the F2 plants are really heterogeneous, you'll have to choose one or a few plants that express the desired traits from your breeding goal (note that with gene dominance, some desired traits may not be expressed in some plants but still be at next generations)
from tese few F2 chossen plants you grow several of their F3 seeds etc...
at each generation you do the same, choose the best plants that matches your breeding goals and grow several seeds from them.
the plants will be more homogeneous at each generation, generally you'll be able to fix a few traits after 3-4 generations (which means F4-F5 could be stabilized for a few traits (like pods shape/color), but maybe not all)
at which generation you'll get a totally inbred line depends on luck and on good breeding choices (if you breed for a trait that rely on codominance, you'll never be able to fix it).
at F7-F9, the variety should be totally stabilized, but it could have been already stabilzed a few years before depending on your luck/choices.
hope that helps