Two main things:
1 - has been mentioned below, which is give feedback. Do it publicly (on their website, LinkedIn, etc.) and if possible give a brief case study. In other words state how you met and how they helped, how your life is better after acting on their advice.
2 - provide a further introduction. Introduce them to another potential advisee, client, or even an expert from they can get advice on a different topic.

Most of the time what the expert wants is to be acknowledged as the expert...that they helped you. They get a strong feeling of satisfaction.

Here's how you can help them feel that way:

1. Thank them when they help you. A few words go a long way.

2. Thank them publicly. Make a video, share a post, write an article...detailing the questions you had and that they helped you with the answer.

You should ask the expert if they're OK with you sharing some details of their responses...they may get paid for their expertise and though they gave it free to you, they make a living that way in other cases. If they don't want you to share anything about what was said, just share the problems you had, and that they did a great job helping you.

3. Take action on their advice, and show them what you did about it.

I can't understate the importance of this. If you ask me for help, and I give it to you freely, and then you go and put it into action and show me what you've done...well, you've got me as a helper for life. I will be so happy for you and delighted you did something about it.

This may counter-intuitively seem like you're "using" the expert, but believe me they want to be used in this manner. When someone takes advice I give them, and comes back to show me, "This is what I did; I ran into these issues," I will shower them with more help. And I will be delighted to do so.

Despite what you may have thought, not many people do anything with the expertise they receive. I have friends who charge large amounts, say $80K, for a few hours of their time to help with specific niche business problems...and the client does nothing with the info. The client is happy: they feel they did something and the investment is an affordable expense to them. But they just don't want to take any further action--not on anything. Too comfy in the comfort zone.

You will note for each of these points I have written a longer and deeper explanation. That is because they have a progression and the feeling of satisfaction for helping you lasts longer in each case for the expert. You want them to feel good for a day or two, thank them when they're helping you. A bit longer, thank them publicly. But if you really want them to feel great about sharing their expertise with you, that their time and energy was well invested, DO AS THEY ADVISE and show them what you did.

When someone comes back to describe problems they encountered when they started doing the thing, it is instantly apparent to me that they have given it a go. That they have taken action on the advice is very satisfying, and I am more than ever in their corner wanting to help them succeed.

As you've seen, you don't have to "share equal value back" from your own field of expertise or buy them lunch or do whatever big thing it is you were imagining. Just do these three things to demonstrate your appreciation for their help, and they will feel great about helping you.

Many times an Expert will run a variety of businesses.

If you get along well with an Expert, ask them about their business portfolio + if you find a fit, you can use their product or service.

1. Say thank you after you are given advice
2. Find something they are wearing and ask them about it. For example, they are wearing a silver bracelet, well ask them about it. Where did they get it, who gave it to them, is it real silver, ext. Being their friend is more than anyone can ask for.
3. Or instead of #2, just say thank you and leave. Let them give to you. Giving is one of the Universe's gifts to us. What we give we receive in abundant amount. So let them give! :)

You can always share the fact that you found someone's advice helpful. Online, you can say something like this:

"If you're ever in need of [blank] advice, talk to [so and so]. They just helped me out with a question I had."

Where? If you have a blog, maybe add a random P.S. If there's a place to leave a review, consider that. Or if you're on social media, maybe share a thumb's up with people. They may not need any advice today, but maybe in a month or a year somebody will. Or maybe a stranger, searching online, will stumble across your thumb's up.