In order for you, the affiliate marketer, to collect the customer's details, you have to make some changes to this process.
To do this, there are a couple of things you need to have.
The first is something to give away (known as an opt-in). It doesn't have to be massive and in fact short can be better, typically a short report in PDF form or even a video. The important thing is that it's related to the affiliate product/s that you're promoting.
For example, if your affiliate product is a weight-loss program, your opt-in could be a PDF or video called The No Situps Abs Workout. You can produce the opt-in yourself or modify a suitable PLR or get someone on Fiverr or Upwork to do it for you at a very low cost.
The second thing you need to have is an autoresponder. You can get started with MailChimp for free. Personally, I use Active Campaign but other popular products are AWeber, GetResponse and ConvertKit.
Then you need to create three landing pages. Your theme may include templates for landing pages. Otherwise, just use regular pages. I find it useful to call them (for example) The No Situps Abs Workout 1: Opt-in, The No Situps Abs Workout 2: Confirmation and The No Situps Abs Workout 3: Delivery. Using this standard groups them together, in sequence of use, in your WordPress page list.
Here's what you put in each:
The No Situps Abs Workout 1: Opt-in This landing page promotes your opt-in product. It will include an image of the product (such as a book or magazine cover) and promotional text covering why the prospect needs it. To get the product, they must enter their name and email address. As soon as they do, they are taken to:
The No Situps Abs Workout 2: Confirmation This landing page thanks the prospect for ordering the opt-in and tells them to check their email's inbox for the download link. But before they do, they should check out... here you have some promotional details of your affiliate offer, together with the affiliate link that you got from your vendor.
The No Situps Abs Workout 3: Delivery This landing page simply contains another thank-you and the link to download the opt-in product.
You can use FileZilla to create a folder on your website to store the opt-in product. Then link to it using its URL. It’s a good idea to store the opt-in product as a zip file as it will then download toyour visitor’s computer when they click on it instead of opening it.
In the background, the opt-in page also connects to your autoresponder, adds the prospect to your mailing list and sends the delivery email with the download link.
Exactly how you do this depends on what WordPress editor you are using. Many paid editors use simple drag and drop to achieve all these requirements. If you are just using the standard WordPress block editor, it can still be done but may require a little extra work.
Research “wordpress editors” to find drag and drop editors. You will see Thrive Architect, Elementor, Divi and others.
So, at the end of this process...
1) You have a new prospect/customer on your mailing list (this is the most important outcome).
2) This prospect/customer has received a gift from you (this engages the psychological state called reciprocity).
3) They may have also purchased the affiliate product (but even if they haven't, you now have more chances to sell them in the future).
Following this process helps to future-proof your business.