Some new pens are stubborn to get started, especially using an ink cartridge for the first time. New pens may have residue from manufacturing that make them difficult to start. So, washing the nib with mild soap and water can help them flow better. Dipping pens and filling them with bottled ink primes the feed. If you only have cartridge ink, try tapping the pen nib GENTLY on a paper towel or rag to start the flow. You might also need to gently squeeze the ink cartridge JUST A LITTLE to start the flow. If you squeeze too hard you'll have a mess. Once you do this the first time and have ink running through the pen from cartridge to tip, you shouldn't have to do it again, especially if you use the pen on a regular basis. If the pen and cartridge run dry and are left sitting for a while, you may have problems again. If you still have problems, try a different brand of ink. My favorite ink for pens with a stubborn flow is Waterman's Serenity Blue. Serenity Blue flows well. It doesn't dry in your nib as quickly as other inks, and it has a beautiful bright blue color.
If your pen has had ink for awhile and clogged, a syringe is really helpful to clean out your pen quickly. Flushing the pen several times with lukewarm water nearly always brings your pen back to write-like-new condition. When I flush a pen, I stand at a sink with a glass full of clean water, drawing the water out with the syringe. Hold the syringe firmly into the pen nib assembly and force the water through, pointing the nib down toward the drain so the inky water is less likely to splatter on you or counter top. Even if you hold them together tightly be prepared to get sprayed.
The nib should be flushed several times until you see clear water coming through the nib. After the nib is clean, use the syringe (empty) to blow air through the nib assembly to help it dry faster. The nib will need to dry - usually overnight - if you want the ink to be full strength. If the nib still has water in it when you re-assemble it, and fill it with ink, the ink will be diluted. Surprisingly, even the tiniest bit of moisture will dilute the ink noticeably.
If your pen still has ink flow problems after cleaning, then you'll need to take apart the nib assembly, remove the feed, and clean the nib and feed with soap and water. When you do this, examine the channel in the feed for ink residue. Use a toothbrush or toothpick to clean out the channel, being careful not to damage the feed. The feed must be clean and the channel open in order for your pen to write well. Some of the better pen and ink dealers sell small copper sheets that can be used to clear the feed channel, even when the pen is fully assembled.