Search array using user input

Your mistake is the case sensitive i in Input

 if (arr[i] == Input) {

should be

 if (arr[i] == input) {

And then you really don't need the else part. Just write the not found alert after the loop and write a return statement inside the if.

function beginhere() {
   var input = document.getElementById("Input").value;

   for (i=0; i<arr.length; i++){
      if (arr[i] == input) {
         alert(arr[i]); 
         return;
      }
   }
   alert("Value not found");
};

And without a loop you can try

function beginhere() {
   var input = document.getElementById("Input").value;

     if(arr.indexOf(parseInt(input)) != -1) {
          alert(input); 
          return;
      }
   alert("Value not found");
};

I've refactored your if conditions, because as for now it alerts result with every cycle of the for loop. If the loop has found the given number inside the array, log the number and return the function (there's no need to keep the loop alive anymore). If not - log that value wasn't found to the console.

var arr = [18, 23, 20, 17, 21, 18, 22, 19, 18, 20];

function beginhere() {
  var input = document.getElementById("Input").value;
  for (i = 0; i < arr.length; i++) {
    if (arr[i] == input) {
      console.log(arr[i]);
      return;
    }
  }
  console.log('value not found');
};

<button onclick="beginhere()">click</button>
<input id='Input'>

Another possible solution, using Array#find.

var arr = [18, 23, 20, 17, 21, 18, 22, 19, 18, 20];

function beginhere() {
  var input = document.getElementById("Input").value,
      res = arr.find(v => v == input);
      console.log(res ? res : "wasn't found");
};

<button onclick="beginhere()">click</button>
<input id='Input'>

You have some issues:

• Move search declaration and initialization inside of the function, because you need the actual value and not the value at start.

• Convert the search value to a number by adding a plus infront of the value. This uses an unary plus + for converting a value (string or number) to a number.

• Test with search.

• Exit function if search is found.

• Display only one message, if not found after the loop.

var arr = [18, 23, 20, 17, 21, 18, 22, 19, 18, 20];

function beginhere() {
    var search = +document.getElementById("search").value, // need to covert to integer
        i; // declaration missing

    for (i = 0; i < arr.length; i++) {
        if (arr[i] == search) { // use search variable
            alert(arr[i]);
            return;
        }
    }
    alert("Value not found");
}

<input id="search" type="text" onchange="beginhere()">