how to align html elements vertically centered

I always use this construction, because it works in all browsers:

<table cellpadding=0 cellspacing=0 border=0 style="width:100%; padding:0; margin:0;border-collapse:collapse">
<tr valign="middle">
    <td><a href=""><img src="img.png" width="200px" height="200px"></a></td>
    <td><input type="text" name="aaa" value="bbb"></td>
</tr>
</table>

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Hi,

I don't recommend to use Table for a form...

I recommend to use Bootstrap it will help you to align things and also this will add responsiveness.

Here is an example of form with Bootstrap
https://getbootstrap.com/docs/4.1/components/forms/

Also they is some helper class to align
https://getbootstrap.com/docs/4.1/utilities/vertical-align/

Bootstrap is more complicated solution, because it requires to load more libraries and makes the web-page loading time longer!
Of course, if author of this question doesn't use bootstrap on his page yet...

Here is the Bootstrap usage statistics
https://trends.builtwith.com/docinfo/Twitter-Bootstrap

Personally I'm not a fan of Bootstrap, though I realize in in the far minority there.  If you're not using it already, then not worth the time and rewrite to implement it.
But please don't use table for layout, very strongly agree with lenamtl on that.

For a simple vertical alignment, you can use this:

.aligned { display:flex; align-items:center; }

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<div class="aligned">
    <a href="" ...> 
     <input type =button....> 
</div>

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I agree, that using different CSS tricks you can achieve this result... But, as you said, for old browsers you need extra code, etc...
I don't see that my code on tables has a bad and old style. Why? Thare is no explanation.
"Table" is standard tag, which supported by ALL browsers of ALL versions. And it works anywhere perfectly!
Somebody tells you, that table displays only when the whole content of inner cells will be loaded... Ok, I agree! But, in our 21 century and fast speeds internet, we will not even notice that!

Pavel, in the case of the code I suggested, the unsupported browsers are exceedingly old. Does anyone still support them on public websites?

There definitely is an explanation why it's bad to use a <table> like that. It's called "semantics," and part of that is only using a <table> when you want multiple rows and columns to display tabular data, like in a spreadsheet.