Being careful with your aim
You can't not radiate, so if you want to not be observed then you need to make sure you aren't radiating in the direction of your nearest neighbours. To do this you'll need to somehow channel all the energy into a series of directional beams that are aimed in-between the stars closest to you. The amount of power you'll need to pump through those emitters will vary depending on the number of emitters you have, so let's have a look at some numbers:
How much energy have we got to lose?
Lets assume we're talking about our sun for now.
OK. Just to be clear that's an awful lot of zeroes.
How can we absorb it?
There are a couple of answers to this, some on this very site. Let's assume that we use a couple of shells to create some vast thermal power plant and we can then shuffle the electricity around. It's not going to be perfect, there will still be some ambient radiation, but with decent insulation and design it should be well below the amount that's noticeable at interstellar distances. If you want to decrease the energy leakage then increase the number of shells (like adding very big, complicated blankets to a very big incandescent baby).
How can we get rid of it?
Let's turn to the ever excellent Randall Munroe for this one.
The Boeing YAL-1 was a megawatt-class chemical oxygen iodine laser mounted in a 747. It was an infrared laser...
There are bigger lasers, but they all fire for fractions of seconds.
So we've got a laser that can fire on the order of megawatts of power. Lets assume they each fire at 3.6MW and we can run them continuously and see how many of them we need...
10^21 lasers. Assuming they each take up a meter squared that's 1/281'th of the space we have to play with on the outside of our sphere. Not great, but it's usable. If we can get more laser apertures in then we can improve upon that, but preferably we want to be able to shift their aim.
Now, if we aim them at the darkest bit of sky we can find from their individual location (parallax is going to be important at these scales), then we'll be minimising our chances of being noticed. Again: This isn't perfect. The lasers won't have perfect beam coherence, so the beam will be more of a cone spreading out into the stars. This in turn means that stars further away might be clipped by an intense and regular source of radiation, spawning all sorts of wild theories about rapidly rotating stars and suchlike.
What about the bits that aren't laser arrays?
Clad them in long wavelength EM absorbent materials, refrigerate them and pump the heat back into the inner shell of your stellar power plant. Sure, you're going to hugely increase the entropy of the system as a whole, but when you're engineering a Dyson sphere I think minimum-entropy concerns are pretty much out the window...
Naturally this has some problems (heat buildup on the laser arrays being a large one) and some potential improvements (the IR lasers probably aren't the best way to direct the energy, some form of particle beam apparatus may well be better) but it should suffice to mask you from a casual observer.
One last note: Make sure the lasers are evenly spread or you'll end up pushing your shell ever so slowly out of position, and crashing a Dyson sphere into a sun is pretty embarrassing...
A quick note: This would also require some 'hotspot' exhausts from which to extract the electricity to power the lasers. Clever positioning of these and suitable focusing systems could again minimise the chance of detection. In fact, if you really wanted to you could probably get away with just using the exhausts, though the focusing requirements would be a lot more tricky to deal with that aiming a laser.