Search Insert - Implementation (The code)

Here's the binary search solution:

function searchInsert(nums, target)
    left := 0
    right := length of nums - 1
    while left ≤ right
        mid := left + (right - left) / 2
        if nums[mid] = target then
            return mid
        else if nums[mid] < target then
            left := mid + 1
        else
            right := mid - 1
    return left

You maintain a search range $[left, right]$. At each step, you check the middle element. If it matches, return the index. Otherwise, move $left$ or $right$ to search the appropriate half. When the loop ends, $left$ is the insertion position.