Here are a few options, depending on how DIY-savvy or actively involved you are in your project:
Rent a disposal bin
They are easily found on-line, under names or keywords such as "construction disposal", and "debris bins".
A "disposal bin" may be known as a "dumpster" in the US, or a "skip" in Australia.
You often pay for a drop-off & pick-up plus a monthly rate. Best to inquire with companies to find out the details, and add it all up based on how long you think your project goes, and how many pick-ups you'll need.
Also find out whether they charge by load (any trip), volume (full/half etc..) or weight (determined by a scale). If by load or volume, note that light debris is usually cheaper to dispose of personally at a landfill or transfer site where they weigh your vehicle upon entry and exit and charge for the difference.
Inquire with your local municipality if there are any restrictions as to where the bin can be placed (on your property, on the street ...) and for how long.
Pile it up in the garage or outside under a tarp, and have a junk removal company load it up as needed. Alternatively, rent a truck and do your own dump runs as needed.
Inquire with your local municipality and/or fire department as to any restrictions for piles of debris on your property. Beware that rain may destroy some of the piled materials to the point that they cannot be re-used or re-purposed, and rain can make the debris heavier which may imply a higher disposal cost.
Purchase a new or used trailer and pile the debris and junk in it to complete your own runs to the dump. Keep it covered with a tarp. Inquire where the garbage transfer sites are, what their rates are (any minimum rates), and whether there is a surcharge for specific types of garbage. For instance, it is not uncommon to require drywall to be bagged according to very specific instructions, and to pay a small surcharge.
If you don't have a hitch, you can rent a car with a hitch for your disposal days.
Sell the trailer after your project is done, or keep it of course if you have the space and appreciate the all-round benefits it offers for projects and hobbies.
In addition to any of the above choices, personally I like to salvage and reuse as much as I can.
This keeps valuable materials out of the dump, and it saves on costs and environmental impacts when materials are reused on site rather than transported to a dump, and then only later to be purchased new.
Lumber is an obvious choice, but some drywall in good condition can be re-used or re-purposed as acoustic insulation.
You can also make may people happy by offering your debris for free on-line (craigslist comes to mind). This is a great destination for windows, doors, cabinets, sinks and other finishings. You'll make some people very happy, and you'll keep it out of the dump.
Take a picture of an item, describe it with a few words, post it, and you'll know within 24hrs whether there is interest.