I'll speak from personal experience while evaluating trial applications.
The most annoying trial applications are those which keep popping up nag screens or constantly reminding me that I'm using a trial. Trials which act exactly like the real product from the beginning till the end of the trial period are just awesome. Limited features are annoying, the only exception I can think of when you could use it is where you have rarely used feature which would allow people to exploit the trial (by using this "once-in-lifetime" needed feature and uninstalling). If you have for example video editing software trial which puts "trial" watermark on output, I'd uninstall it as soon as I'd notice it. In my opinion trial should seamlessly integrate into user work-flow so that once the trial ends they would think "Hey, I have been using this awesome program almost each day since I got the trial, I absolutely have to buy it." Sure some people will exploit it, but at the end you should target the group which will use your product in daily work-flow instead of one time users. Even if user "trials" it 2 times per year, he will keep coming back to your product and might even buy it after 2nd or 3rd "one-time use".
(Sorry for the wall of the text and rant)
As for how to improve the first session. I usually find my way around programs easily, but one time only pop-up/screen (or with check-box to never show it again) with videos showing off best features and intended work-flow are quite helpful. Also links to sample documents might be helpful. If your application can self-present itself (for example slide-show about the your slide-show program) you could include such document. People don't like to read long and boring help files, but if you have designer in your team, you could ask him to make a short colourful intro pdf. Also don't throw all the features at the user at the same time. Split information into simple categories and if user is interested into one specific category keep feeding him more specific information. That's why videos are so good, with 3-6 x ~3-5 minute videos you can tell a lot. Also depending how complex your program is you could include picture with information where specific things are located on the screen.
Just my personal opinion, I have never made a trial myself. Hope it helps.