Link exchange can come in many ways.
About decade ago it was viral to create page /friends.html or /partners and just link out to those who linked to you in exchange.
Needless to say, in 2018 this idea sounds strange.
Now let's take 3-way link exchange. Webmaster of a site A links to your site B and for this you link from your site C to his site A. That's a better solution until you make it obvious that was an exchange.
I believe that the best of the safe link exchange methods is :
1. find a website with similar or higher metrics DA, DR, traffic in a similar niche, but not your competitor that builds links with guest blogging.
for example, if your site is swimming pool cleaning services, your potential partner would be a swimming pool seller, or home cleaning services. Relevant, but not competitor.
2. write them a short but sweet email offering to write a guest post at your blog and in return ask them to write a post on their blog.
You'll have a chance to build 2-5 high quality relevant links for free and safe.
Sure, if you're trying to get maximum out of a throwaway site, this method isn't for you. I believe, that doing link exchanges on scale with irrelevant and trash sites won't help even in short term.
Hope that was helpful, wish you good luck with your rankings!
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