Let's go to practice by copy paste following html script into one file:
Welcome to My Homepage
This is Intro
This is paragraph
Another ParagraphSome list:
After saving file just open it using google chrome or firefox with firebug installed. This post will consider using google chrome only. If you are using other browser please adjust accordingly. Following is rendered page from above html script.
From that console we can start play with jQuery. Just type "jQuery" to make sure jQuery setup properly. If showing like this than it already setup properly.
By the way this post assume that you have internet connection because jQuery library referenced in html is loaded from CDN on internet. If you don't have internet connection make sure you download jQuery js file and referenced accordingly in src script attribute correctly.
Let start to use id selector type jQuery('#choose') in console. It will show the result below the script we type.If jQuery cannot find the tree it will show empty bracket  since selector found empty element.
Let's try to select element directly using jQuery('li') . This will select all three elements of li tags.
Next let's play little bit with filter and start to play with manipulation. Type this inside the console jQuery('li:first').css('color','red'). This script will select first li in document and set it css property color to red. Final result can be seen below:
Ok that's all for now. We can see more complete capability of jQuery by reading its API at http://api.jquery.com