When to apply for visas
Check your visa requirements as far ahead as you can as you will have enough on your plate as you approach your departure date.
The best place to get your relevant visas are either through the embassy directly or through a visa processing company. Some travel agencies, like STA Travel, will also arrange certain visas for you if you are lucky.
Most pre-departure visas can only be applied for up to 3 months before you enter that country and then the validity starts from that date. Examples of these are the Russian, Mongolian, Chinese and Vietnamese visas.
Working visas are even more important to obtain and should be looked into well before you purchase your flight tickets in case there are any complications.
Australian visas
The ETA (Electronic Travel Authority) for Australia is a god-send for travellers as it can now be done over the phone, by email and now arranged online and costs next to nothing (free if arranged directly through the embassy but very time consuming to get hold of them). There is no paperwork (don't worry you still get the stamp in your passport!) and gives you 3 months to stay as a tourist only (no work).
Next: Applying for a passport