Use the TTABlog for the Tricky Part. As you can see, accessing the documents isn't difficult. The challenge is finding those trademark applications that match your situations so that you crib from the right docs. In other words you want to piggyback on the work of another applicant who succeeded with similar facts. One way to find cases similar to yours is at the TTABlog which covers the proceedings of Trademark Trial and Appeals Board (TTAB). We recommend searching the blog for terms similar to the ones in your objection -- for example if your mark is alleged to be "geographically descriptive," search for that term and copy the relevant serial numbers for the trademarks in dispute.Check the responses in those TDR files.
Objections and Objections. BTW, you indicated you wanted to file a response to an objection against a trademark application. We're not sure which type of "objection" you're referring to but we're going to assume you want to respond to an examiner's Office Action refusing or rejecting your application. (Here's a helpful system for responding.) The public (including competitors) can also file objections to your trademark application during a thirty day period following publication of your mark in the Official Gazette. That requires different formalities, though it may involve similar language and legal arguments.
Thinking Like an Examiner. Finally, the Dear Rich Staff recommends that if you're curious as to the starting point for examiner objections, you should review section 1200 of the Trademark Manual of Examining Procedure. It's available online and is searchable by topic.
This just in ... MR, one of our readers, followed up with this helpful tidbit: TTAB opinions and docs never show up in the TDR, but can be obtained at TTABVUE, if you type in the application or registration number, proceeding number, or other identifying material. The most the Trademark Office databases will do is post a notice in the TARR status database, noting that an opposition has been filed. There is a very handy database maintained at TTAB Across the Board, which allows you to type in phrases like "geographical descriptiveness" in the Search Documents box, and get a list of TTAB cases where that shows up, and clickable access to the specific documents.