If you know the name of the monk whose scratchpad you'd like to see, you can first navigate to their home node (by e.g. clicking on their name in the chatterbox), then click on the 'View' link next to the word Scratchpad:.
If you are in a place for typing monastery content (such as a node or the chatterbox), you can enter [pad://username] and this will rendered as a link directly to their scratchpad. For example, [pad://vroom] results in vroom's scratchpad.
Alternatively, there is one node which allows access to any scratchpad by username: the scratch pad viewer. You can go there and type in a monk's name. Or, if you're making a URL, you can write ?node_id=108949;user=username (If the link is for use off-site, be sure to include the http://perlmonks.org/ part. ;-)
Same as above (using your own username, of course). But in addition, if you type [pad://], it results in a link that says my scratchpad. However, this works only in the PerlMonks messaging system (private messages and chatterbox), not on nodes.
You actually have two scratchpads: a public one and a private one. The above discussion relates to public scratchpads only. Private scratchpads are hidden from mere mortal monks (i.e. gods can see them, because they see all).
Editing your public and private scratchpads is done all on one page. You can update one or both in one submission. To get there, simply go to your home node and click 'Edit' next to the word Scratchpad:. (The 'Edit' link takes you to the same node as the 'View' link, but the scratchpads are ready for editing; this is controlled by the addition of displaytype=edit in the URL.) If you're already viewing your scratchpads, you can enter edit mode by clicking the 'Edit' link which appears just above the current public scratchpad content. When you're done editing, click the 'Submit' button.
Now, there are a few more tricks.
If you have your Personal Nodelet enabled,
there will be a couple of links at the bottom of that nodelet, saying
"Add to public / private pad".
If you click one of these links,
it inserts a link the current node (whatever you're viewing at the time)
at the bottom of your public or private scratchpad, respectively.
This can be handy if you like to use your scratchpad for maintaining lists of bookmarks.
(Go to Nodelet Settings to enable your Personal Nodelet.)