If you are getting serious about sewing and are looking to finish garments with a really professional seam, I'd highly recommend an Overlocker machine, its a quick and easy way to finish your seams.
They can be really frustrating at first, I remember spending 4 hours trying to thread my first pen and nearly gave up, but once you know how its pretty easy.
I have an old Janome machine, I bought it second hand for £70 and it works perfectly fine.
Something that took me a while to figure out, is that once you have overlocked the seam, you will still have to secure the overlocked thread to stop them from unravelling, so this quick blog post explains how to do this easily, all that you will need is a darning needle.
Ok, so you have finished your seam allowance using your preferred method (on this sleeve I have finished each seam separately as it needs to be pressed open, you will need to ensure that you leave overlocked thread "tails" at the end of each overlocked seam as below...
Next, take your darning needle and carefully insert it into the overlocked edge with the eye of the needle on the outside and the tip poking inwards but sticking out at the other end as shown below...
Now, insert the thread "tail" into the eye of the needle, you may need to dampen the end of the thread slightly so that you can get all the threads through the eye.
Now pull the needle through the overlocked edge so that the tail follows, you may need to use a little force but do it carefully.
Next, snip off the excess tail (the bit that isn't inside the overlocked edge).
Voila! All done, the thread is now secure and will not unravel! You just need to repeat that on each end.
It may add a few minutes onto your sewing time, but I can assure you that it is much better than it unravelling in the wash!
If you have any questions just as in the comments below.