How to open a file / browse dialog?

Use this.

<script>
  function openFileOption()
{
  document.getElementById("file1").click();
}
</script>
     <input type="file" id="file1" style="display:none">
     <a href="#" onclick="openFileOption();return;">open File Dialog</a>

Create input element.

Missing from these answers is how to get a file dialog without a input element on the page.

The function to show the input file dialog.

function openFileDialog (accept, callback) {  // this function must be called from  a user
                                              // activation event (ie an onclick event)
    
    // Create an input element
    var inputElement = document.createElement("input");

    // Set its type to file
    inputElement.type = "file";

    // Set accept to the file types you want the user to select. 
    // Include both the file extension and the mime type
    inputElement.accept = accept;

    // set onchange event to call callback when user has selected file
    inputElement.addEventListener("change", callback)
    
    // dispatch a click event to open the file dialog
    inputElement.dispatchEvent(new MouseEvent("click")); 
}

NOTE the function must be part of a user activation such as a click event. Attempting to open the file dialog without user activation will fail.

NOTE input.accept is not used in Edge

Example.

Calling above function when user clicks an anchor element.

// wait for window to load
window.addEventListener("load", windowLoad);

// open a dialog function
function openFileDialog (accept, multy = false, callback) { 
    var inputElement = document.createElement("input");
    inputElement.type = "file";
    inputElement.accept = accept; // Note Edge does not support this attribute
    if (multy) {
        inputElement.multiple = multy;
    }
    if (typeof callback === "function") {
         inputElement.addEventListener("change", callback);
    }
    inputElement.dispatchEvent(new MouseEvent("click")); 
}

// onload event
function windowLoad () {
    // add user click event to userbutton
    userButton.addEventListener("click", openDialogClick);
}

// userButton click event
function openDialogClick () {
    // open file dialog for text files
    openFileDialog(".txt,text/plain", true, fileDialogChanged);
}

// file dialog onchange event handler
function fileDialogChanged (event) {
    [...this.files].forEach(file => {
        var div = document.createElement("div");
        div.className = "fileList common";
        div.textContent = file.name;
        userSelectedFiles.appendChild(div);
    });
}

.common {
    font-family: sans-serif;
    padding: 2px;
    margin : 2px;
    border-radius: 4px;
 }
.fileList {
    background: #229;
    color: white;
}
#userButton {
    background: #999;
    color: #000;
    width: 8em;
    text-align: center;
    cursor: pointer;
}

#userButton:hover {
   background : #4A4;
   color : white;
}

<a id = "userButton" class = "common" title = "Click to open file selection dialog">Open file dialog</a>
<div id = "userSelectedFiles" class = "common"></div>

_{Warning the above snippet is written in ES6.}

Unfortunately, there isn't a good way to browse for files with a JavaScript API. Fortunately, it's easy to create a file input in JavaScript, bind an event handler to its change event, and simulate a user clicking on it. We can do this without modifications to the page itself:

$('<input type="file" multiple>').on('change', function () {
  console.log(this.files);
}).click();

this.files on the second line is an array that contains filename, timestamps, size, and type.

Here's is a way of doing it without any Javascript and it's also compatible with any browser.

EDIT: In Safari, the input gets disabled when hidden with display: none. A better approach would be to use position: fixed; top: -100em.

<label>
  Open file dialog
  <input type="file" style="position: fixed; top: -100em">
</label>

Also, if you prefer you can go the "correct way" by using for in the label pointing to the id of the input like this:

<label for="inputId">file dialog</label>
<input id="inputId" type="file" style="position: fixed; top: -100em">

you can't use input.click() directly, but you can call this in other element click event.

html

<input type="file">
<button>Select file</button>

js

var botton = document.querySelector('button');
var input = document.querySelector('input');
botton.addEventListener('click', function (e) {
    input.click();
});

this tell you Using hidden file input elements using the click() method

I worked it around through this "hiding" div ...

<div STYLE="position:absolute;display:none;"><INPUT type='file' id='file1' name='files[]'></div>

How about make clicking the a tag, to click on the file button?

There is more browser support for this, but I use ES6, so if you really want to make it work in older and any browser, try to transpile it using babel, or just simply use ES5:

const aTag = document.getElementById("open-file-uploader");
const fileInput = document.getElementById("input-button");
aTag.addEventListener("click", () => fileInput.click());

#input-button {
  position: abosulte;
  width: 1px;
  height: 1px;
  clip: rect(1px 1px 1px 1px);
  clip: rect(1px, 1px, 1px, 1px);
}

<a href="#" id="open-file-uploader">Open file uploader</a>
<input type="file" id="input-button" />

These days you can also use the File System API

https://developer.mozilla.org/en-US/docs/Web/API/File_System_API

It allows for file browsing, and can go deeper to offer functions like saving of files too. Here is a demo, although it requires a secure context and can't be used in a cross origin iframe:

    <a href="#">Pick a file</a>
    <p>File name: <span id="file-name">None</span></p>

    <script>
      async function getFile() {
        // Open file picker and destructure the result the first handle
        const [fileHandle] = await window.showOpenFilePicker();
        const file = await fileHandle.getFile();

        document.getElementById("file-name").textContent = file.name;

        return file;
      }

      document.querySelector("a").addEventListener("click", () => getFile());
    </script>

I know this is an old post, but another simple option is using the INPUT TYPE="FILE" tag according to compatibility most major browser support this feature.