First off, the best resource that you have for your sewing machine or serger is your owners manual. You'll find a section of your manual is dedicated specifically to maintaining your machine. Depending on the machine you have, you may find information on oiling your machine, cleaning the exterior of the machine, or cleaning the shuttle. My overcast serger manual also includes information on replacing lightbulbs, and changing knives.
If you don't have access to your machine manual, many makers have downloadable manuals available on their websites.
Your machine manual is really important, because not every sewing machine needs the same care. My sister in law just recently purchased her first sewing machine, it's an entry level brother, and needs to be oiled bi-monthly, or weekly if used more frequently. My brother doesn't require oiling, due to the construction of my machine. I am currently waiting (not very patiently) for a replacement bobbin shuttle. While I don't have to oil my machine, I do need to make sure that the shuttle doesn't get scratched. So basically, if you haven't already, it's time to familiarize yourself with your sewing machine and it's manual.
If your machine does require oiling, here is a great post from Craft Nectar on cleaning and oiling your sewing machine. Also note, that not any old oil is suitable for your sewing machine. It's best to go to a sewing supply store and find some specific to sewing machines.
If possible, push the dust out and away from the machine. Obviously there are places in a sewing machine that are hard to reach. A vacuum with very small attachments is a great way to remove material. Some people use compressed air, but you need to be very careful when doing so, as to not lodge any material in the sewing machine parts.
This is a great post on how to clean a brother 1034d serger, it includes instructions for oiling it as well.
The exterior of your sewing machine or serger can be wiped down with a washcloth and some mild dish detergent and water. Make sure that all cords are unplugged before cleaning your sewing machine.
While you have out your mild detergent, you might as well clean your iron. I think that it is all of the fusible web that I use, and probably some spray starch, but my iron gets DIRTY. I found this great article on cleaning your iron. Using just the first of her recommendations on cleaning the sole plate or the iron, my iron went from this.....
|After washing with mild detergent|
...to this. Big improvement. I'd recommend cleaning the reservoir of the iron prior to cleaning the plate, I didn't, and then had to clean the plate again.
Now I just need to tackle this beast. I have no intention of trying to remove the stains, I think that a new cover is in order. Here's a great tutorial on making your own ironing board cover.