I understand you have some scripts recorded using Selenium IDE. You can execute these recorded scripts on BrowserStack by pointing the hub URL to Browserstack's Selenium hub ‘http://hub.browserstack.com/wd/hub’ along with your username and Automate key. Your 'username' and 'automate key' can be found at Account --> Automate, after you have logged in to your account.
I would suggest, you refer to the comprehensive documentation on BrowserStack Automate. It takes you step-by-step through the product and all its features. You can select the language you are using and get started with BrowserStack Automate.
If you have any more questions, feel free to email at firstname.lastname@example.org. They will be happy to help you out.