Good comparison of the companies:
PSA is the top dog but they are crazy backed up and only open for their premium tiers which are expensive.
I believe BGS, which is the 2nd most respected, is in the same boat.
SGC has good turnaround times and is cheaper. Definitely the best new challenger to the top 2, for sports at least. You'd have to check values for other cards.
There is also CSG, which has a good reputation in Comics and other collectible grading but just started doing cards. Could be good for Garbage Pail Kids but not sure.
Choose a company, go to their site, and follow their instructions to send the cards in. Pretty standard and the instructions are detailed, might need to buy Card Savers but it varies by company.
https://www.amazon.com/Card-Saver-Holder-Graded-Submittions/dp/B078SFLTJQ
Use 130point to search eBay to find values of certain cards in grades from each company:
Search eBay Sales for Sports Cards, Memorabilia and More | 130 Point
What to look for before sending a card in:
Sports Card Grading 101 Guide
Other random links:
Create Shipping Label - PayPal
https://www.amazon.com/Ultra-Pro-Sleeves-8-Inches-100-Count/dp/B0002TT3N4
https://www.amazon.com/Ultra-Pro-Resealable-Sleeves-Holder/dp/B00BUVFB16
Let me know if you have any specific Qs, would be happy to answer