In following, let's state that xpathLocator is Selenium 1 locator, while xpathFinder is more or less By.xpath(xpathLocator),selenium is instance of Selenium, driver is instance of WebDriver (FirefoxDriver).
Is an element present on a page ?
Selenium 1:
selenium.isElementPresent(xpathLocator);
Selenium 2:
driver.findElements(xpathFinder).size()>0;
Get HTML source of a page
Selenium 1:
selenium.getHtmlSource();
Selenium 2:
driver.getPageSource();
Is a text present on a page ?
Selenium 1:
selenium.isTextPresent(text);
Selenium 2:
driver.getPageSource().contains(text);
Go to relative URL
The relativeUrl is URL relative to initial URL, i.e. without the "http://hostname".
Selenium 1:
selenium.open(relativeUrl);
Selenium 2:
driver.get( initialUrl + relativeUrl );
This call is blocking, i.e. further processing is stopped until the page is loaded.
To open an URL relative to the currently used one, use driver.getCurrentUrl():
driver.get( driver.getCurrentUrl() + relativeUrl );
Is an element visible on a page?
Selenium 1:
selenium.isVisible(location)
Selenium 2:
((RenderedWebElement)driver.findElement(location)).isDisplayed()