In short, ignore the basic genetic machines to start with, the acclimatiser need only ever be used once and is of zero value after (but don't worry, it'll chew up a lot of your time when you DO come to use it - though it helps to know that you only ever need put sand and ice into it, don't bother about the other resources, those two'll give you max tolerance to everything if you put in enough), and the sequencer is just plain rubbish (it lets you make "templates" of bees, but only of the first few races; it doesn't work on, say, imperials).
The advanced machines are excellent, but they rely on serums, and those require royal jelly (produced by imperials) to make the vials. Sorry, but bee machines won't help you get that species; from there though, it's up up and away.
Get the genepool and start filling tanks with your spare drones. Do this early, even if you don't have any serum vials or the other machines that use the liquid DNA this produces yet. When you can make the vials, get the isolator and start throwing in drones (NOT princesses) and empty serums. Specifically, you want to throw in bees with max fertility and the shortest lifespan traits.
Ignore the replicator, it's a waste of a diamond unless you want to give serums to other players. Your synthesiser and purifier will eat liquid DNA, so hopefully you've got a reserve saved up by the time you build them - the bit about waiting until the purifier says it's done is important, don't just wait until the serum quality is reported as "excellent", it'll end in tears. Always perform synthesis prior to purification.
The inoculator randomly applies the trait in the serum to either the active or inactive side of the bees you put in at random (whizzball's off the mark in saying it always does the inactive trait first). Because you want both traits done, expect to use about four serum charges per bee on average (minimum of two). Don't innoculate queens, the drones they produce may not get the effects - instead, fully innoculate a princess and then drone before breeding them together.
To apply all this to getting new species, take a princess and drone of the two parent races - say you're aiming for industrious, you'd get diligent and unweary - and fully inoculate them with shortest lifespan and max fertility. Let the two pairs breed with their matching race a few times over until you have a stack each of identical drones.
Then, take a princess of one type and run it through an apiary with drones of the other type and a set of soul frames. Analyse ALL the results, not just the ones that come out looking like industrious, and throw all the drones with the desired race as a primary and/or secondary trait into the isolator. Any drones produced that aren't industrious get thrown into the gene pool.
If you get the industrious serum, well done, pump it up to about 8-10 charges and inoculate a max fert/shortest life princess and drone with it (remember those stacks of drones you made? Breeding ANY princess with them over and over will quickly turn it into a clone of them, which'll then start producing drones you can ADD to the stacks...). Now empty the serum vial and put it back into the isolator - create a new drone stack, and use THAT to convert further princesses.
If the new race has any other traits you want (eg a new effect), keep going with the soul frames until the resulting drones have given you all the serums you want. Apply that to an old drone and princess (ones with other good traits on 'em) along with the new racial serum, then breed them together over and over to produce a new drone stack. The princess used to produce the new race should be bred with that stack (or some other one) to stamp out all the undesired traits the new species introduced. You'll quickly find that attempting to use the bee machines to "fix" the traits on every new species is a complete waste of time - drone stacks let you modify multiple traits on a princess at once, serums can only do them individually. Because you'll always be wanting to create new stacks, don't throw out your apiarys once you start building alvearys - those smaller hive boxes are great for drone production.
If you DON'T get the industrious serum, put the princess back into the apiary and crank out another four drones. There's no harm in doing this while waiting for the isolator to do its work, assuming you don't mind wasting soul frames.
It's a very good idea to grant a rocky princess and drone max fertility as soon as you can, as these work during rain, at night, in caves, and have a respectable tolerance to temperature and humidity. Produce a stack of drones, breed them with other princesses to create clones, then inoculate new racial serums over the top of the results. Boom, a new race with all the benefits of rocky bees, plus any other decent traits you happen to throw in over time...