The solution is pretty easy actually:

<button style="border:1px solid black; background-color: transparent;">Test</button>

This is doing an inline style. You're defining the border to be 1px, solid line, and black in color. The background color is then set to transparent.

The solution is pretty easy actually:

<button style="border:1px solid black; background-color: transparent;">Test</button>

This is doing an inline style. You're defining the border to be 1px, solid line, and black in color. The background color is then set to transparent.

UPDATE

Seems like your ACTUAL question is how do you prevent the border after clicking on it. That can be resolved with a CSS pseudo selector: :active.

button {
    border: none;
    background-color: transparent;
    outline: none;
}
button:focus {
    border: none;
}

JSFiddle Demo