Dust

Dust is one of the biggest annoyances with renovation. There are many sources for the dust, including existing dust (eg. in the roofspace, under the floor) that is disturbed, new dust that is created from breaking up existing materials (eg. knocking down or cutting into walls), and new dust that is created from new material (eg. sawdust, plaster dust).

Safe Zones
The first strategy is to maintain safe zones that are sealed off from the bulk of the renovation. Any room will do, but if you have a room or rooms that do not require much work, then these will be the best choices. We chose our bedroom, dining room, and a storage room off the kitchen. The aim is to prevent dust from entering those zones. This can be done by keeping the doors closed, sealing any gaps under the door, and taking off footwear when entering those zones.

Protect your valuables
Although you've created a safe zone, it's impossible to keep all of the dust out. Buy lots of dropsheets (you can get cheap plastic ones from your local hardware warehouse, like Bunnings) and cover appliances and areas that need protecting from dust. Store food in large sealable plastic boxes.

Air Filters
There are a large number of air filters on the market, such as IQAir and BlueAir. Ensure you obtain one with a HEPA filter. Many filters also have activated carbon to absorb chemical fumes and VOCs, which I would recommend if you plan on using chemicals such as polyurethane (eg. for sealing floorboards) or paints that are not low-VOC. You can move the air filter from room to room. I would recommend running these in the room you are residing in, and also wherever you happen to be vacuuming (which disturbs lots of dust and won't catch all particles). Air filters can either be hired, or purchased. As an aside, they are also good for filtering out air pollution (which can be higher inside than out), and allergens. For those reasons, and because of the duration of our renovation, I decided to purchase rather than hire. For those in Australia, Air-Iononics seems to have a good supply. Make sure to order yours a few weeks before renovations are due to start, as there can be a lead time.

You can also get good filters for ducted heating/cooling systems, so if you already have this in place, then investigate this option.

Vacuuming
You can hire or buy vacuum cleaners with HEPA filters. It is a good idea to mop the floor before you vacuum, as this will minimise the amount of dust that becomes airborne when you vacuum.

Asbestos
One can't talk about renovation without mentioning asbestos. All I can say is, seek professional advice on this before you begin, especially if you're doing the reno yourself. There is no point doing a renovation if you're not going to be around to enjoy the results.