How to center links in HTML

there are some mistakes in your code - the first: you havn't closed you p-tag:

<a href="http//www.google.com"><p style="text-align:center">Search</p></a>

next: p stands for 'paragraph' and is a block-element (so it's causing a line-break). what you wanted to use there is a span, wich is just an inline-element for formatting:

<a href="http//www.google.com"><span style="text-align:center">Search</span></a>

but if you just want to add a style to your link, why don't you set the style for that link directly:

<a href="http//www.google.com" style="text-align:center">Search</a>

in the end, this would at least be correct html, but still not exactly what you want, because text-align:center centers the text in that element, so you would have to set that for the element that contains this links (this piece of html isn't posted, so i can't correct you, but i hope you understand) - to show this, i'll use a simple div:

<div style="text-align:center">    
  <a href="http//www.google.com">Search</a>
  <!-- more links here -->
</div>

EDIT: some more additions to your question:

• p is not a 'function', but you're right, this is causing the problem (because it's a block-element)
• what you're trying to use is css - it's just inline instead of being placed in a seperate file, but you aren't doing 'just HTML' here

The <p> will show up on a new line. Try wrapping all of your links in one single <p> tag:

<p style="text-align:center;"><a href="http//www.google.com">Search</a><a href="Contact Us">Contact Us</a></p>

you would put them inside a <p> or a <div>

<p style="text-align:center">
    <a href="http//www.google.com">Search</a> 
    <a href="Contact Us">Contact Us</a>
</p>

sample: http://jsfiddle.net/X8HM4/1/

Since you have a list of links, you should be marking them up as a list (and not as paragraphs).

Listamatic has a bunch of examples of how you can style lists of links, including a number that are vertical lists with each link being centred (which is what you appear to be after). It also has a tutorial which explains the principles.

That part of the styling essentially boils down to "Set text-align: center on an element that is displaying as a block which contains the link text" (that could be the anchor itself (if you make it display as a block) or the list item containing it.