Drop contingencies. Sellers looking to move quickly want as few obstacles as possible. One way to do that is to omit contingencies on your offer. The last thing a seller wants to do is go through all the steps of selling and then have to put their house back on the market because the contingency deal fell through. Discuss which contingencies may be reasonable to omit with your real estate agent.
Be flexible. Motivated sellers love flexibility. For example, a seller may want to delay the closing date to let their children finish the school year before the move. Others may wish to move as soon as possible because they have a job waiting for them in a new city. Whatever the case may be, being flexible with these situations is a bonus for many sellers.
Make it (just a little) personal. It's helpful to reveal a little about yourself to the seller --but not too much. You can provide a short explanation of why you chose this particular house over other homes, such as because it reminds you of your childhood home or you grew up in that community and want the same for your children. Whatever the reason, share it to let the seller know you're the right buyer.
Don't mention any plans to remodel the house. Keep renovation plans to yourself. While sellers may realize that you'll make changes to the home, they don't want to hear about it most of the time. The seller may have invested thousands of dollars in fixing up the property, so they certainly don't want to hear about plans to undo their work.