What is your application here?
If you wanted to just ping it in your browser, you could load up https://api.twitch.tv/kraken/channels/25295503/subscriptions
where 25295503 is your channel id.
To get the ID of other channels/users, you’ll need to hit the Twitch API Users endpoint and pass in the name. I made a chrome extension to do this: Twitch Username and User ID Translator
Because this endpoint is sensitive, you’ll need to load it along with a header that identifies you as a verified person/program to access it. To do this, you’ll need to “inject” the oauth that identifies you into the request you’re making. I recommend 3ventic’s Client ID injector which also injects oauth.
Of course, you’ll also need to to get the oauth. You can do that yourself via setting up your own application and using the application flow to get the oauth. You can also use a tool to generate you an oauth token under the tool’s application. For that matter (shameless plug) I recommend TwitchTokenGenerator.
Again, you’ll need the oauth scope: channel_subscriptions