1) Financing - This is a big one, as it's one of the most common reasons sales fall though. Having a pre-approval from a good local lender can make the difference. When you can show sellers you are financial prepared to purchase, this provides them confidence which often means you can pay less.
2) View the property in person, possibly more than once. Offers that are "site-unseen" are looked on negatively, as they have a much lower rate of reaching completion. Serious buyers make the drive to see what they are buying.
3) Be flexible where you can - Sellers often choose offers that align with their needs, not simply those with the highest price. Possession dates and included items can be a deal breaker.
Thinking about these will get you started, but there are many other ways a good Realtor can help strengthen your offer. Questions? Give me a call, I'd be happy to guide you.