L.A. Noire/Buyer Beware
Walking down the street, you'll hear gunshots and run to the crime scene. Since you are the first respondent to the crime scene, you'll take the lead in the investigation until the detectives show up, while the other cops keep a perimeter for you. This is your chance at a break-out case that will earn you your detective's badge.
 Nunn Bush Shoes
Start off by investigating the body. When searching bodies, you will usually be able to look at the head, arms and coat pockets. Move your finger over the body part you want to look at to investigate further. In this case there's nothing in the victim's right coat pocket, but in the left you'll find a layaway voucher belonging to a C. Galleta showing the payments being made on some pearl earrings. By the body you'll find some .32 caliber shell casings and in the trashcan on the sidewalk you'll find a gun. Turn the gun to read the model and serial numbers along the left side of the barrel. When you've found those three clues, you should hear the chime that means you've found everything, and the investigation music will fade out.
Before you leave, talk to the guy in the orange shirt that told you he called the cops. He'll tell you he heard the shots and saw a girl run back into the shoe store when he looked. This will give you another person of interest, so head into the store to talk to her. Miss Galleta will introduce herself and you'll find out that the victim, Everett Gage, was her boss. When interviewing people, select your questions from the list in the notebook. Here you only have one question to ask, and when you do, note that she can't meet your eyes after making her statement, indicating she may be lying. You know from the layaway voucher that the earrings were for her, so bring this up by accusing her of lying and presenting the voucher.
Choosing the right response gives you a new person of interest, and opens up two more dialogue options you can use. Ask her about the possible murder suspect next. She fingers Kalou as the shooter, but she's still looking somewhat nervous. Use the Doubt option to press her further, and find out that Mr. Gage hated Jews, which gives Kalou motive for the murder. Ask Ms. Galleta the last question and note that her face looks how it normally does when you're not asking a question, so you can select Truth to coax more information from her.
With the interview done, head out to the car and set your next destination. Although you can skip the gun store, evidence you find there can be used when you interrogate Kalou. Following up on every lead will also help you close cases valoriously as a detective.
 Eagleson's Gun Store
Although the store owner didn't sell the gun, he does remember that Edgar Kalou serviced it there and he'll give you Kalou's workplace. You can now tie Kalou to the gun.
 Hartfield's Jewelry Store
When you walk in, the guy behind the counter says he'll go get Kalou for you, but when you runs you know it was him all along. Chase after him by hopping the counter and running him down. In this chase you'll be able to use a warning shot to stop him early if you want.
 Police Station
Back at the station with Kalou in custody, Captain Donelly will speak to you. He likes the way you've handled the case so far and wants to give you shot at breaking Kalou and getting a confession. For this interview, if you mess it up you'll get to do it over and over until you get it right, so don't worry about choosing the wrong responses. If you found all the evidence and got everything you could out of the girl at the shoe store, you'll have plenty to of ammunition to use against the suspect.
Start off by asking Kalou about his argument with Gage. He denies any involvement in the shooting, but since you have an eye witness testimony, this is an easy one to challenge. Select Lie and present Ms. Galleta's positive identification. From his response, he'll give away his religious motivations, so ask him about that one next. He says he doesn't know anything about Gage's hatred for Jews, but since Ms. Galleta mentioned it and he called Gage a Jew-hater before, it's obvious he's lying. Select Doubt to press him on this further and you'll have everything you need to charge him with the murder.
The Captain is impressed with your skills and tells you to get a couple suits pressed. Your next case will be as a detective on the Traffic desk.