How can I tell if my solenoid is going bad? When I hit the start button it makes a clicking sound on cold starts. After its been running it fires right up.

 

99% of the time, the battery is low on its charge.
Hook up a voltmeter to the battery when youre starting, and watch the voltage drop when you hit the starter button. If it drops lower than 10 volts...either the battery needs a charge, the terminals are oxidized, or the battery is about to fail.
Charge the battery up, and if it continues to click...have the battery load tested.

 

I just put a brand new battery in. One the first start up it did this when the hit the start button. I hit the start about 3 times and then it fired right up.

 

A new battery can be faulty, just because its new doesnt mean its perfect. The load test is the only way to determine if a batttery is good or not.
Check to make sure the contact area, between the terminals of the battery and the cables, is shiney( scuff it up with sandpaper or a file), and the connection is tight.
Sometimes new batteries need a charge before they are put into use, so try charging it up.