Here is a small example of custom search bar 
1. Go to storyboard, take TextField place it at below navigation bar (we will type text here to find any string)
2. Set delegate of TextField

Come to ViewController class now

Create IBOutlet of TextField eg -

@IBOutlet weak var searchText: UITextField!

Now declare 2 array globally one for storing all  element and second for storing result of filtered data

var filteredArray:NSArray = [] //to store filtered data
var shoppingList:NSArray = [] //to store whole data  

In “viewDidLoad” define your array

override func viewDidLoad() { 
        super.viewDidLoad()
        shoppingList = ["Eggs","Fruits","milk","Rice","Vegetables","Milk","oil","apple","pear","banana",
            "raspberry]//you can place dynamic data instead of this 
        // Do any additional setup after loading the view.
    }

 After this we will do some code inside “shouldChangeCharactersInRange” to know string type by user

func textField(textField: UITextField, shouldChangeCharactersInRange range: NSRange, replacementString string: String) -> Bool{
        let string1 = string
        let string2 = searchText.text
        var finalString = ""
        if string.characters.count > 0 { // if it was not delete character
            finalString = string2! + string1
        }
        else if string2?.characters.count > 0{ // if it was a delete character
     
            finalString = String(string2!.characters.dropLast())
         }
        filteredArray(finalString)// pass the search String in this method
        return true
    }

    
func filteredArray(searchString:NSString){// we will use NSPredicate to find the string in array 
        let predicate = NSPredicate(format: "SELF contains[c] %@",searchString) // This will give all element of array which contains search string
        //let predicate = NSPredicate(format: "SELF BEGINSWITH %@",searchString)// This will give all element of array which begins with search string (use one of them)
        filteredArray = shoppingList.filteredArrayUsingPredicate(predicate)
        print(filteredArray)
   }

By above lines of code we will get our matched result, Now it’s time to display this searched result in controller 

 For this , go to storyboard 

1. Now take a tableView  and set a prototype cell in it and place it below  the TextFiled(we will show search result here) .

2. Set Delegate and DataSource of TableView.

3. Place a label inside your prototype cell, and give IBOutlet of this label in your UITableViewCell (ShoppingDataViewCell in this case)

eg: @IBOutlet weak var searchResultTxt: UILabel!

Now come to your ViewController class 

Take  IBOutlet of your tableViewCell , eg:

@IBOutlet weak var tableView: UITableView!

Now do some line of code in DataSource method of TableView

func tableView(tableView: UITableView, cellForRowAtIndexPath indexPath: NSIndexPath) -> UITableViewCell {
 let cell:ShoppingDataViewCell = tableView.dequeueReusableCellWithIdentifier("ShoppingDataViewCell", forIndexPath: indexPath)as! ShoppingDataViewCell
        cell.searchResultTxt.text = filteredArray[indexPath.row] as! String
        return cell
}

func tableView(tableView: UITableView, numberOfRowsInSection section: Int) -> Int {
    return filteredArray.count;
}

And don’t forget to reload you TableView inside this  “filteredArray(searchString:NSString)” function

func filteredArray(searchString:NSString){// we will use NSPredicate to find the string in array 
        let predicate = NSPredicate(format: "SELF contains[c] %@",searchString) // This will give all element of array which contains search string
        //let predicate = NSPredicate(format: "SELF BEGINSWITH %@",searchString)// This will give all element of array which begins with search string
        filteredArray = shoppingList.filteredArrayUsingPredicate(predicate)
        tableView.reloadData()
        print(filteredArray)
}

Now run your app and you will see output like below.