If a home is listed, a good approach to the seller is to go directly throught the seller's listing agent.
This way the same agent is working as list and sale agent and this can prove more reasonable and efficient should you need to negotiate for the agent to recieve commission on the monthly lease.
If the house is not listed go directly to the owner. Be reasonable and appreciative of their time, engage with a suggestion and allow them time to consider. Be willing to move on and be willing to keep looking, as many sellers don't have the financial option to lease and these sellers will be unable to help you.
However, in the current market some sellers do have serious incentive to do this, so, this is a strategy becoming more and more prevalent. You may consider getting an option along with the lease. Good Luck.
The benefit of having an Agent represent YOU, is that he or she can make these calls for you on your behalf.
More and more lately homes that are offered for sale end up renting for many reasons. However, if the Owners need to sell to move forward you would have your Agent look for properties to rent that suit your needs.
As the other agents have stated, contact the listing agent to see if a rental is possible.
it never hurts to check with the listig gagent to see if you can find one that is willing to consider a rental.