If you intend to drive from Queenstown to Te Anau, you need to start off early at about 7am. The journey to Te Anau takes about 5 hours on average and passes through a lot of desolate areas including plains, deserts and farms.
Hence fill up a full tank before you go and get some food/drink supplies because in between Queenstown and Te Anau, there are not many places along the way to stop.
If you want to fully experience Fiordland, then you can stay overnight in Te Anau before entering the park.
There are many places by the lake which offer budget-to-moderate accommodation. You also need to fill up your petrol as there are no petrol stations in the park and the journey is about 80 kms to the sound.
Instead of taking the long journey by bus, if you have the budget, you can choose to fly instead.
However this option is not for the budget conscious. The flight is approximately 20 minutes and offers breaktaking scenery of the mountains and sound in Fiordland.
However you can do a combo where you can choose to fly to the Milford Sound and return back to Queenstown by bus or vice versa.
Check out the travel info counters in Queenstown for more information and brochures. They advertise frequently and quite a few people do this sort of thing for a different experience.
As Te Anau is the last town before entering Fiordland, make sure you get whatever you need at this town before you do so.
Obviously since this is a National Park cum World Heritage Site, you won't find convenience stores, petrol kiosks anywhere in there. Hence fill up a full tank before you venture it.
There is nothing worst than an oversight that could really spoil your day. And no one will tell you this and check up on you before entering. Hence, use your brain.
In winter, bring snowchains before entering fiordland. There will be warnings and guards stationed to advice you to put them on, if you need to.