As far as I know, designers work mostly with bricks only.
They do have a desk and a quasi-unlimited supply of parts (which I think is actually not too exactly close to their desks), and usually use their imagination the same way a fan does.
Something which fans don't do however, and which designers must do, is keep track of the price of the model they're building so that it's in line with the expected price point (these are determined by marketing when a theme is started).
This is much more complicated than it sounds, because element prices aren't always logical (for example, a Technic axle 5 is cheaper than a 4), and the number of different elements counts too (that's why sometimes they use other parts than what would be logical, such as a 1×2 brick with groove when the groove has no purpose whatsoever at that place, but since the brick is already included elsewhere and a regular 1×2 isn't, it's cheaper to use).
In short, all production costs are taken into account, including packaging and so on. Of course, for parts which aren't produced yet, the prices is much higher, but how higher depend on a lot of factors (whether the part exists but not in that color, whether the parts fit well in the system, and so on). Design teams may also want to bargain with other teams to have them support the cost development of a new part. Licensed themes may have a different cost structure because the licensees are sometimes willing to pay for a new part if it makes the model more realistic (most good hairdos come from licenses nowadays).
Once the designer has a model ready (it'll undergo quite a few tweaks along the way, of course), they'll hand it to another team which will be responsible for making sure the model can be built by kids, and possibly tweak it some more to make the instructions clearer (ever noticed why some hidden bricks have sometimes unexpected colors?). These guys do use computers, and they'll make the instructions as well; but in the meantime the designers are busy on their next model.