In this tutorial we'll clean up said signature up and make it ready to drop in any document.
Step 1: Open the signature file.


Notice the jagged edges and "gaps" in the lines.
Step 2: Change the image mode to RGB if it's not in that mode already, by going to IMAGE > MODE > RGB.
Step 3: If the signature is on a busy background, or isn't black, go to IMAGE > ADJUSTMENT > LEVELS. Drag the black arrow to the right, and the white arrow to the left, so that all three arrows basically sit near the middle, as shown below.
This increases the contrast, and should make the background white, and your signature solid black.

Step 4: Go to FILTER > NOISE > DUST & SCRATCHES. Pick a pixel size that gets rid of the "gaps" in the lettering. I used 2px.

After applying the dust filter
Step 5: Now we're going to separate the signature from the background layer. Right-click the signature layer (should be the only one - the background layer) and click "Duplicate layer". Name it whatever you want, and delete the background layer that you just copied.
Step 6: Using the magic wand tool (seen below), with the "Contiguous" box UNchecked, and a tolerance of 32, click somewhere in the white part of your image. This will select all the white you've got.

The magic wand tool
Step 7: Let's smooth this thing out. Go to SELECT > MODIFY > SMOOTH and pick a pixel amount that will smooth the signature without distorting it. This might take a few tries, depending on what resolution you're at. I used 5 pixels.
Step 8: If your signature is thick enough to shave off a little, go to SELECT > MODIFY > EXPAND and expand by 1 or 2 pixels. Now hit the delete key to kill all that white and leave you with a transparent background.
If your signature is thin, click CTRL + SHIFT + I to invert the selection, then go to SELECT > MODIFY > EXPAND, and expand by a few pixels. This will make the selection bigger. Now go to EDIT > FILL and fill with black. Invert the selection again and hit the delete key to get rid of the white background.

Not the most glamorous tutorial, but I hope you find it useful.

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