You will often see articles on business news sites offering brief snippets of what Buffett or other popular managers have been buying. Of course, these articles won't give you the details you're looking for if you're trying to dig deeper in order to understand more about the purchases and sales. Fortunately, you can do it yourself quite easily.
Every quarter, Berkshire is required to file a form (titled 13F) detailing its holdings. Three days ago, Berkshire filed its 13F for the quarter ended September 30th. You can access this form as follows:
1) Go the Edgar page for Berkshire Hathaway filings
2) In the "Form Type" search box, type "13F" (without the quotes)
3) Open the 13F-HR filings and scroll to the holdings section
This process isn't unique to Berkshire; you can use it to track any "institutional money managers" of US public companies that invest at least $100 million in securities. There are also sites out there (like gurufocus.com) that aggregate this data for several managers, and provide it in easy to read formats.
Keep in mind, however, that there is a time lag. Since the filing covers up to September 30th, we have no idea what Berkshire bought in October, even though this filing took place in November.