As I can see it u have to small errors in ur code. First u try to search for an element before it's in the dom. So this "document.getElementById("count")" will not return the element.
The other part is for a onclick to work u should ad a ";" after the function name like this.
<input type="button" value="+" id="plus" onclick="plus();">
But then the element still wont get updated by clicking the button. So therefore u should include the script and rewrite it like this. What I have done is binding the onclick event on the element in the javascript at the same time as I create the function. I also changed so the variables are declared with one var and the code is wrapped in a self executing function so nothing is declared in the global scope. I hope my answer helped u some, good luck!
HTML
<div id="input_div">
<input type="text" size="25" value="0" id="count">
<input type="button" value="-" id="moins">
<input type="button" value="+" id="plus"">
</div>
<script>
(function(document){
var count = 0,
countEl = document.getElementById("count"),
minus = document.getElementById("moins"),
plus = document.getElementById("plus");
plus.onclick = function(){
count++;
countEl.value = count;
}
minus.onclick = function(){
count--;
countEl.value = count;
}
}(document));
</script>
Here is a link to my fiddle to test the code.