As this article illustrates, the grading process can be quite overwhelming. There are a ton of things you need to purchase, many steps that can be confusing, and trying to figure out if the condition of your cards is “grade-worthy” is something that is best left to a person who has a lot of experience and the proper tools.
There are many people who specialize in “group submissions”. You can send these people your cards and they will handle the entire grading process for you for a small fee. They will look through your cards for you, clean them (remove fingerprints, dust, and sometimes even be able to buff out small surface scratches, etc), and put them under a microscope to determine if they are grade-worthy.
The advantages of sending your cards to somebody who does these group submissions are that even though they charge you to inspect your cards, they will often save you money by rejecting the ones you shouldn’t bother sending out.
For instance, if you sent them 20 cards instead of sending those same 20 cards directly to PSA, and they decided that only 10 of them are worthy of being sent out, they just saved you 10 x $15-20 in grading fees ($150-$200) for typically around $3/card ($60). They will also handle the entering of the cards into the grading company's database.
Finally, you will often receive your cards back a little bit faster when you go this route. If you are submitting cards on your own, you won’t have access to the same pricing and turnaround times as people who do group submissions. PSA’s $20 economy service is no longer available to individuals unless you join their “Collectors Club” for $59/year.
In short, if you have never submitted cards for grading, I would highly recommend going with a reputable group submission. It will likely result in you getting better grades, faster turnaround, and will likely even save you money in the long run. I have sent many cards to Card Collector 2 and yielded fantastic results.