[VulgarDisplay]

I just bought a Weller 25watt pencil soldering iron.  The ST3 tip that came with it was too big to work on a PCB so I picked up an ST6 and ST7 tip to use with it.  Now for some reason these tips do not get hot enough to do anything.  I noticed that the smaller tips don't fit as snug into the soldering iron.  I put them on the desired connection I'm trying to make on my first cmoy and even after about a minute the solder will not melt.  I'm tinning and cleaning the tip before I try and heat the connection, but the iron just doesn't seem to get hot enough. 
 
Do I need to buy a higher wattage iron or what? This one just isn't cutting it for some reason.  

 

[gimble]

Heat transfer is proportional to surface area. You just switched to smaller tips.
 
I found this a bit tricky at first too...I don't have any real advice other than to practice a bit, you should get the hang of it quickly enough. Filling a spare chunk of protoboard with jumper wires ought to do it.
 
Actually, two bits of advice. Eutectic solder is awesome, especially if you have an adjustable iron. And DIP sockets are much less prone to damage in the hands of an amateur than an IC is (and helpful if you want to experiment with different op-amps).

 

[VulgarDisplay]

I just decided to pick up some slightly bigger tips.  The numbering system on their professional series soldering tips is idiotic by the way.  ST1 and ST2 are on the way now.  Hopefully they help.  I've already decided that this first CMOY isn't really going to work (most likely).  It's ugly, and some of the joints are dull.  I got enough parts to build a few so this one is for soldering practice.  

 

[gimble]

Your first project is almost unavoidably going to turn out to soldering practice...even if you follow my suggestion and start on some wire.
 
Desoldering braid is good to have if you don't have some yet, and cheapish. If nothing else, you're probably going to put something in backwards at some point. Probably several times.
 
If you've ever coded before, you probably know exactly what will happen. It's a simple task - in theory - but minor mistakes are both inevitable and capable of completely breaking the entire system.

 

[Avro_Arrow]

Do yourself a favor and pick up a WES-51.
It's a great entry level soldering station and
can often be found on sale. Mouser has it
for $134 but I bet you can find one for less
than $100 on sale someplace. Just keep
your eyes open.