When I go looking for a new tool it’s because I have a new problem (or a problem has gotten too big to ignore any more!), so my first step is going to be thinking about what the problem I really want to solve is (looking at root-causes and deciding where I need need a tool to gather more information or intervene in a process). Then I’ll look around for solutions and my first pass will probably include:
- Does it sound like it has the features to help me?
- Does anyone I know say it’s good?
- Is it used by a lot of people?
- Does it get good online reviews?
- Relative costs vs features of available solutions.
- Bring this info back to my team for feedback.
Then I’ll give it a go and see if it works for me/us. Will start on a small scale and go from there.
I usually find it doesn’t take long to decide if there are any showstoppers to using a new tool. A day or two maybe, and after that I guess I’m going to keep using it until it starts not delivering what I need (as our needs change) or something better comes along.
The biggest turn-off when evaluating a new tool would be negative feedback from people I know. But also, no easy access to a free trial is also a big hurdle.
(Oh, and it better be pretty intuitive, 'cause let’s be honest, there’s no way I’m reading more than a couple of paragraphs to get started! 
Although tips along the way are welcome. )