1. Go to Novelupdates for light novels (or Mangadex for manga) and look up the Japanese character name of the series)
2. Go to Google Translate and paste "https://booklive.jp/", then open the link.
3. Paste the series name into the search bar and click Search.
4. Click on the desired LN/Manga series (if applicable). Note how I had to do step 3 in a browser tab not using Google Translate before pasting that URL back into Google Translate.
5. Click either Buy Now or Add to Cart depending on how many books in the series you want to purchase.
6. Scroll down to see all the books in the series. Add the ones you want to cart.
7. Once you are done, you can click on the cart in the top right and proceed to purchase.
8. Booklive will prompt you for email registration. Enter an email and follow the instructions.
As far as purchasing goes, that's something I think you can figure out for yourself. To be honest, Google Translate makes this pretty painless, but if it doesn't end up working on the purchase urls, just copy paste the page text into Google Translate and see what's going on. If there's an error or information message of some sort that you can't copy, just right click on it and Inspect Element. Then you should be able to find the corresponding JP text and plug it into Google Translate.
I will upload a video demonstration for the pre-purchase steps sometime in the future.