How do I set <table> border width with CSS?

Doing borders on tables with css is a bit more complicated (but not as much, see this jsfiddle as example):

table {
  border-collapse: collapse;
  border: 1px solid black;
}

table td {
  border: 1px solid black;
}

<table>
  <tr>
    <td>test</td>
    <td>test</td>
  </tr>
</table>

The default border-style is none, so you must specify that as well as the width and the colour.

You can use the border shorthand property to set all three values in one go.

Also, the border attribute describes the border for the table and the cells. CSS is much more flexible so it only describes the border of the elements you are selecting. You need to select the cells too in order to get the same effect.

table, th, td {
    border: solid black 1px;
}

See also border properties and tables in CSS.

The reason it didn't work is that despite setting the border-width and the border-color you didn't specify the border-style:

<table style="border-width:1px;border-color:black;border-style:solid;">

JS Fiddle demo.

It's usually better to define the styles in the stylesheet (so that all elements are styled without having to find, and change, every element's style attribute):

table {
    border-color: #000;
    border-width: 1px;
    border-style: solid;
    /* or, of course,
    border: 1px solid #000;
    */
}

JS Fiddle demo (Or using shorthand border notation).