How can I pass a service variable into an Angular Material dialog?

For passing variables you can grab the instance of the component opened in the dialog, from the MdDialogRef instance returned in the MdDialog.open() method call.

dialogRef = this.dialog.open(PizzaDialog, config)
dialogRef.componentInstance.<property_name>

Modified Pizza from the github material2 docs angular material doc

@Component({
  selector: 'pizza-component',
  template: `
  <button type="button" (click)="openDialog()">Open dialog</button>
  `
})
export class PizzaComponent {

  constructor(public dialog: MdDialog) { }

  openDialog() {
    let config = new MdDialogConfig();
    let dialogRef:MdDialogRef<PizzaDialog> = this.dialog.open(PizzaDialog, config);
    dialogRef.componentInstance.name = "Ham and Pineapple";
    dialogRef.componentInstance.size = "Large";
  }
}

@Component({
  selector: 'pizza-dialog',
  template: `
  <h2>{{name}}</h2>
  <p>Size: {{size}}</p>
  <button type="button" (click)="dialogRef.close('yes')">Yes</button>
  <button type="button" (click)="dialogRef.close('no')">No</button>
  `
})
export class PizzaDialog {
  name:string;
  size:string;
  constructor(public dialogRef: MdDialogRef<PizzaDialog>) { }
}