After deciding where to go, the next step is research. Although some people just want to get up and go, I think doing at least some research gives you a better experience. Travelling overseas is expensive and you want to get the best value and see and do the things that really appeal.
I am planning a trip to Thailand so my research involves lots of searching the web and talking to others who have been or people from Thailand. You could also look in the local library or pick up some brochures from travel agents. The larger newspapers also have a weekly travel section (Sundays for the Brisbane Courier Mail).
The first important information I am seeking is when to travel. In Thailand, for example, the Thai peninsular (which includes Phuket) has different climatic conditions depending on whether you are on the east or west coasts. It is best to avoid the rainy season in either location. Once you decide when it's time to start looking for flights.
There are many websites such as Lifehacker giving tips for finding the cheapest flights. Most of these sites say booking as far ahead as possible gives you the best prices. You can book flights up to 12 months in advance. Of course if you are flexible with dates and destinations you can take advantage of last minute deals, however if you rely on this strategy you may miss out or end up with flight times that do not suit. Another useful suggestion is to book directly with an airline rather than a third party website.
Booking accommodation is the next step, as you now have dates to work with. My strategy is to decide what are the really important attributes and work from there. For example in Bangkok I want a hotel close to a skytrain station and with a swimming pool. Once again there are many websites to help you choose. I find Hotels Combined really useful. From there you can check availability, prices, hotel information and most importantly read reviews from other travellers.
If you decide to use a travel agent you can take your hotel preferences with you so they can include those in your package. In my experience travel agents will offer accommodation at the hotels they have an affiliation with which may well suit you. If however you have your heart set on a particular hotel they should be able to work with this.
The next step is to research some additional information about the place you are visiting. This will include attractions - when are they open, how much are they, anything else you need to know. It is also useful to have some background information about the country you are visiting. I now know in Thailand it is considered rude to point your feet towards people, and if you say anything negative about the royal family you could be in some trouble.
Once you have covered all of this make sure you have a passport valid for at least 6 months and any visas you need. The Department of Foreign Affairs and Trade website can help with this. Then it's up, up and away on your fantastic holiday.
I travel extensively and my travel "bible" is Trip Advisor - I do nearly all my research there using both the hotel reviews, but more importantly the travel forums for each destination. There is a mine of valuable information in the forum's - for my trip to Goa last November, the info I got about where to stay and what to do was invaluable. I also now contribute back to Trip Advisor with reviews, I know how much they help me so am happy to pass on my experiences to others in return. And so pleased to see you mention DFAT - not only are they great for visa information, but also for travel advice - and don't forget to register your trip with them via Smart Traveller - that was if anything were to happen they have details of where you are - never leave home without completing that info on the DFAT website.