Eucs are really quite easy to grow from seed compared to a lot of other woody plants and trees, and not all that fussy. The seed sprouts as readily as that of many common annuals and perrenials. It is important to use a light potting mix of relatively neutral pH that will not pack down or get crusty on the top. Beyond that, there is really nothing particularly difficult about it.
The seed should be sown on top of the soil surface, and then covered with a fine layer of sand, just enough to keep the seed from being exposed to the light. (A fine layer of soil can also be used, but the use of sand greatly diminishes the risk of damping off.) Like most other seeds, they need to be kept moist but not wet. Using bottom heat to raise the soil temperature is not necessary, and in fact hinders germination of some of the alpine species.
The ideal germination temperature is around 65°F for the forest species and 60°F for the alpine species. The more tender, showy-flowered species listed on this page from warmer regions of Australia should probably be kept at a temperature of 70°F or so to germinate, and should not be stratified.
It is important that the seedlings be placed in bright light immediately after germination. The seed may be started indoors, but it must be moved outdoors, or into a very sunny window, immediately after they begin to sprout. This can present a difficulty for a hobbyist wishing to start the seed in winter.
The seed can be sown individually in pots, but since they are so small and rather difficult to handle, I usually sow a large number of seeds in one small (4" or so) pot. They can then be popped out of the pot all together, separated, and potted up individually. Planting them in larger flats or seed trays also works, so long as your medium is light enough that all the roots come up without breaking off.
The time to separate them or prick them out is when the first pair of true leaves (after the cotelydons, which are the first two seedling leaves) have fully expanded and the second is showing. (However it is also OK to wait a little longer than this.) I suggest potting them directly into 1-gallon pots, but smaller pots can also be used so long as they are to be planted out even sooner after that.
If they are grown in the spring, they should be ready for planting out (10 - 14" tall) in about 10 - 18 weeks from when the seed is sown. Plan on about 12 - 14 weeks for most species. This is important to know so that you can have plants ready at the right time of the year.
If larger plants (16 - 20" tall) are desired, pot them into 2 gallon pots when they reach about 5 - 6" tall, taking care to straighten any roots that have reached the edge of the pot and grown sideways. Once they reach about 20 - 24" tall they should be planted immediately, or their growth will be set back.
Multiple branches should have regenerated from the wound and from below ground level. Select three or four of these (choosing strong, well-spaced branches), and remove all other branches completely, cutting them back to the base.
Year three and onwards:
Allow sideshoots to develop from the chosen branches, removing only those sideshoots that are too low and dragging on the ground, or are crossing, rubbing or otherwise badly placed.
Remove any excess new stems arising from the base.
Occasional thinning of congested side branches may be necessary as the bush matures.
Established trees require little pruning other than the removal of any dead material.