Do your research
In order to get the very best deal, you need to know what the market value of the home is. Once you have a fair market value, take into consideration the condition of the home itself and what it's worth. For example, some concessions that may warrant a lower offer is lack of parking, poor location, old home and more.
As well, assess your bargaining power. What is the state of the market? How long has the property been on the market? An owner who is desperate to rent their property will be willing to negotiate.
Be confident and courteous
Remember, this may be your future landlord! You want to start off the relationship on a good note and they will most likely be more open to negotiations if you build a good relationship right off the bat. Don't be afraid to tell the owner a bit more about your story and what kind of tenant you are. Avoid lowball offers as this may offend the owner or put them off completely.
This one may seem obvious, but it's worth saying. Work with the owner to see from their point of view and make fair concessions. Try to be reasonable and accommodate when you can for the owner, for example if they would prefer an earlier move-in date or longer length of tenancy. The more appealing and easier the tenancy will be for them, the more likely they are to accept an offer.
Don't be afraid to let the owner see from your point of view and understand your reasoning behind the offer. The more of an understanding both parties come to, the quicker you can both come to an agreement.