Updated at 05 Jan 2022
There are multiple ways to tackle a Telegram channel promotion. Usually, people think that it's about finding relevant and not groups to spam links to their channels or groups. Some reasons why spamming doesn't work: You steal people's attention and intrude on your offering. Who would like that? Usually, you violate a group's rules. It's highly ineffective. You publish a link, get banned shortly. Some people who saw the link don't care because your channel isn't relevant to them. Or, they came there to spam too.
If you don't have a channel yet, create it on Telegram. Promotion isn't about spamming, but growing your presence online and on other Telegram channels. Your channel's content should be great, of course, but we have issues with discoverability. Many people may find your channel good enough to subscribe but it's hard to even find it. There are multiple ways to search for channels.
People go there and type what interests them. Make sure you have the right channel name, so it can be discovered through the native search. Does it have the necessary keywords that people would use? Use them in the description too. When you're searching for something, you use the global search of Telegram and it's quite empty. Not helpful. For example, if I were to search for a channel about automobiles, Telegram would show me two channels that have my search phrase in the channel handle(e.g. @cars), one or a few bots. Will it help me to find the right channel? Probably not. Even though, adjust your channel handle and description to be discoverable.
Sumary: this method won't help you much if you have a lot of competitors.
Those are the websites where people add various Telegram channels. The sites filter them by category, so it simplifies browsing. I recommend you to add your channel there too. Google for "telegram catalogs" and add it to the top 5. My usual statistics for new subscribers is the next: ~50% of people come from the search, ~50% come from the catalogs. You can see the analytics in your channel native stats provided by the messenger. It's placed at the "New followers by source" section. The top 2 sources for me are "URL" and "Search", where "URL" is an indicator of catalogs. Sometimes I may get 90% of people to come from the catalogs. It depends on the channel exposure there. For example, you may get featured, or, people search for some keyword more often. It's hard to predict because the algorithm relies on external websites and their ranking on search engines.
Many catalogs get forgotten quickly and only the top ones will serve you for a long time. You may buy ads in the catalogs to feature a channel. However, you'll get spike traffic. Also, people there search for different channels and only a small part of them would be interested in a channel you promote.
Sumary: Telegram catalogs are a steady source of followers. For my channel, I get 15-200 new subscribers a day. The average is about 22 per day. It'll differ for your channel because of the topic.
There are channels like yours, so you might get exposure there through cross-promotion. How it works:
In such a way, you and the other channel will get new subscribers.
You decided to promote your Telegram channel for free, I see. However, you might hear about putting ads on other channels. It's almost the same as cross-promotion, but it's only you who order ads, the other channel's owner is only interested in money in return. The con of such an approach is that it gives you spike traffic, but for money. You can't predict how many people will subscribe to your channel, even having all the statistics.
The most important thing in promoting your Telegram channel(for free or not) is to get more exposure. Hence, people can find your channel. It's difficult to do find something in the native Telegram search. It's also difficult to rely on the catalogs' attractiveness for people. However, the more constant traffic you get, the better. Spike traffic is not so good because of its variability. Today you got 20 subscribers, and tomorrow you may get 0. Rely on the constant traffic sources such as Telegram catalogs. Or, do periodic cross-promotions with other channels' owners.
I want to cover Telegram channel exposure in more detail in the future. Currently, it's laughable to rely only on catalogs and ads. It reminds the pre-modern marketing situation: companies meant advertising by marketing and promoting anything. You got ads, you get people. It won't work in the long-term perspective.