Determine if UPC or EAN numbers will serve your intended purpose. Because of the logistics of the industry, legitimate sellers cannot allow returns, as they would not be able to sell them again without risk. While most retailers readily accept UPC and or EAN, some of the big ones have rules and restrictions that may apply to your product.

Determine how many you will need. Each unique product will need its own number. So if you have an item that comes in two colors, you will need two numbers. If your item comes in two colors and 3 sizes, you will need six, three for each color.

On the GS1 official website, verify that your numbers are legitimate and that the licensee name and Prefix given you are the ones on file with GS1 (the barcode global authority): GS1 verification
You need to do nothing further re: registration of your numbers. There is no "global" registration for each product. Instead, you will just need to provide each of your retailers/wholesalers with your numbers and their accompanying info (description, size, color, etc.). Again, check with them first and get it right.
You will need to generate barcode labels. Again, refer to your retailers/wholesalers to make sure you know the right size label with any required text.
You can print labels with your own computer: You will need

your printer or a label printer (well under $100 on Amazon)
software (usually free with printer)
labels in rolls or sheets (about 1 cent each from Amazon, Office Depot, etc. )

You can also have a service print your labels (google "barcode label printing service")
We strongly recommend that you use a barcode scanner ( $14 and up on Amazon) to test your labels before affixing them and shipping out your products.

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UCC (renamed GS1 US in 2005) is the barcode "authority" in the US. It used to sell licenses for the use of the first part of a bar code (the "Prefix").
Until 2003, a business could buy a license from UCC for a Prefix and it could then use the next 5 digits to number up to 99,999 of its products. It was perpetual and with no annual renewal fee.
In 2003 UCC changed its pricing to a per barcode number license fee, with annual renewal fees.
This created a market for those pre-2003 businesses to "sell" (assign) their excess numbers from their 99,999. That is what you are buying today if you are not buying directly from GS1 and paying their prices.
The assignments carry the same terms as when originally issued: perpetual and with no renewal fees.
Most barcode numbers sold on line are from resellers to whom a pre-2003 license holder assigned its numbers, possibly through a number of re-sales (assignments) before they reached today's reseller. In some cases they are not even legitimate numbers-they have just been made up, copied, or inadvertently used already.
Tracking the chain of ownership (license assignments) of barcodes sold by resellers is not always possible and there is the risk of A Barcode Horror Story

Barcode Info - "Must Knows"... before you buy your UPC codes