How can I buy property without my own money?
It's tough to buy a property NO MONEY down however you can do it if you find a very motivated seller that is willing to do seller financing. That being said alot of times they'll want some money down to ensure if you don't pay the mortgage they get something out of the deal besides the property they're trying to sell back.
That being said it isn't all that hard to buy a property with very little money down and then get that money out of the property within the first year.
If you are looking to owner occupy the property and you're a first time home buyer you could get something with as little as 3.5% down using a FHA loan and if you ask the seller to pay closing costs you'd be into it for not alot of money. If you find a great deal that you can purchase of less than 75% of the After Repair Value (ARV) then you can refinance it into a conventional mortgage after 6 months to a year and take your money out. Then you own the property with none of your money in it.
If you are not looking to owner occupy then you need to look for sellers that are very motivated, property probably needs to be on the market for a good while, and get them to pay your closing costs and if possible (depending on loan type) some of your downpayment. Try to find a bank (probably a credit union) that will lend you the majority of the money. Then you just have to come up with the difference. Ideally you'll get it at a price below market value (hence the need for the motivated seller), and have some equity in the property once you close. Then after 6 months to a year you refinance the property based on it's appraised value and pull your money back out.
You can also try the BRRRR strategy using hardmoney or seller financing to cover the downpayment / repair costs but you will need to find a very solid deal somewhere in the 50-60% ARV range to get the parties you need comfortable with the property/process without needing to put any of your own money into it.
I know this is quite a bit of information, hopefully some of it helpful, but just throwing idea's out there since the question is very vague and unsure exactly what you are planning to do. Once you get a few deals under your belt and can use equity from prior deals to fund new ventures it's much easier to buy without dipping into personal savings.
@Ro Young Jonathan's advice above is great. To add, one of the first ways I've bought investment property without my own money was bringing in a partner. The partner put in the 25% downpayment and I put the loan in my name. We split everything 50/50 after.
Hope that helps.