To make a case against Emily, what you need to do is present all of the evidence, as noted by witnesses and the townspeople (who, after all, did narrate the story).
Here is the evidence that works to prove Emily guilty:
1. She bought rat arsenic from the druggist. You can approach the druggist and bring him to the stand to testify of her purchase, and of the fact that she refused to answer the question that he asked her, "What is this poison for?" This puts the murder weapon into Emily's hands.
2. Get a concise timeline of Homer Barron's disappearance. Get eyewitnesses who saw him go into Emily's house by the back entrance. Note that no one saw him leave, but that they assumed he did. This proves he was in her house, and that he disappeared shortly thereafter.
3. Get the neighbors who reported the awful smell to testify of the smell, and establish about what time after Homer's disappearance that the smell occurred. Get the aldermen who applied the lime to testify of when they applied it. Then, bring in a forensics person to give a timeline of a decaying corpse, and about when it would begin stinking, and match it up with the timeline of the smells from Emily's house.
4. This will be the most difficult part of the case to prove, and that is motive. Have witnesses recall how she refused to give up her father's body. Then, have witnesses recount how Homer "wasn't the marrying type" and preferred the company of men. Use these two bits of evidence to paint a picture of Emily as deeply disturbed, and unable to face rejection from yet another man; use that to paint her as demented enough to murder a man just so he won't abandon her again.
With all of that evidence above, you should have a pretty good case against her. Good luck!