Once the legislative session gets going, you can get most of the information you need to track what's happening (if not always as quickly as you'd like it) from the capitol website, including the House and Senate websites, which collectively are so robust and useful I consider them a true state treasure. This allows nearly the same access to information as is available to those actually attending public hearings, including online posting for most events and real time and archived video of committee hearings and floor debates.
A good way to specialize is to to track the agendas and watch the hearings for the handful of committees covering some particular issue area from week to week - in my case, criminal justice, but you could do similar things on healthcare or schools or beer distribution or whatever you're interested in. You'd quickly find there are a lot of interesting tidbits coming up in the process that never make it into MSM accounts.
It's easy to search for bills by topic or bill number from the main capitol website page or you can identify bills you're interested in from the General Subject Index, which usefully categorizes them when they're filed. (See a good explanation of how to track bills through the process.)
When analyzing bills, Google is your friend. Frequently the same issues will have been debated in previous sessions or in other states. All Texas statutes are available online so you can read the text of the law where the bill would be inserted. The Legislative Reference Library's Index to Sections Affected will tell you which parts of the code you need to look at.
You can check upcoming committee hearings each week in the House and Senate. For example, tomorrow at 8 a.m., House Appropriations will meet and listen to a budgetary overview on criminal justice and transportation issues, while on Wednesday at 8 a.m. the Transportation and Homeland Security Committee will hear testimony regarding the Department of Public Safety and border security.
There's a free, personalized bill tracking and alert system - MyTLO - where you can sign up for bill and meeting alerts - essentially the same logistical information a lobbyist needs to do their job. You can get email alerts when the committees post their agenda each week, then triage the bills to identify ones you care about for blogging purposes. Then you can watch the video record from the House and Senate websites in real time or at your convenience later in archived format.
Armed with that information and supplemented by other news and blog accounts, it's possible for bloggers to independently track the process and add strong supplemental coverage to MSM reporting that adds to instead of just parroting or competing with dwindling capitol coverage.
I was asked recently by a national reporter whether blogs and grassroots media would grow enough to counteract the shocking decline in political reporters assigned to cover daily legislative beats. I replied that it was conceivable, but not particularly likely. It's a rare, compulsive editorialist who tracks legislation in that much detail if someone's not paying them to do it.
On criminal justice topics, our state suffered a significant loss when John Moritz of the Fort Worth Star Telegram took a buyout last year and left the capitol press corps. He was among the relatively small number (count 'em on one hand) of capitol reporters who routinely covered criminal justice legislation in significant detail, so now there will be one fewer pair of experienced eyes watching the process and less information available for the rest of us.
Similar gaps arise on other issues every time a newspaper or TV station reduces capitol staff. Blogs can't by themselves solve this problem for the same reason the MSM has trouble in the online medium: there's no business model to sustain the work. But episodically, in any given niche, blogs can and do mitigate some of the loss.