Go with the grain to prevent splinters
Routing curves typically causes tearout along wood end grain. Routing against the grain on curves causes splinters. You can reduce tearing on end grain by going with the grain wherever possible. Plan ahead to divide your strokes so that each pass will be feeding in a direction that gives you the advantage. For the vertical grain shown, plan to feed to the top of a curve, stopping there. (The hand router is shown pointing away, as if you were looking through the machine. The table router is fixed facing up and the lumber is feeding past it.)
Routing pine softwood, veneer or stringy luan plywood is difficult. If a bit digs in, the wood grain will split and tear out. For a tactile demonstration of how it happens, roll up a paperback book so it is fanned outward. As you stroke your finger across the edge of the curve, it feels silky and sounds like a zipper. If you drag against the curve, it feels rough and catches. You want the bit to enter so the soft layers ahead of it compress together.
Prior to cutting out a blank or putting on a template, orient it on the wood grain for the most advantage. If your layout has horizontal grain, you could manage it another way, as seen here. A re-arranged perpendicular layout is not always a favorable option. Consider where it would be logical to flip the board over. It's less trouble to methodically re-apply a template than to re-do problem curves ruined by blowout. Reversing the action can also be done by switching between hand and table. Difficult curves could be completed by a drum or spindle sander.
Occasionally, you may find it useful to clamp a backup board tightly against the end. Then, after routing to the end of the workpiece, you can continue past its edge and on into the scrap lumber. The backup board contains and compresses the fibers that would otherwise split off.
Laminate chip-out
Always route through the laminate into the substrate. This way the backing supports the thin top layer or veneer, which would chip off if you went from back to front. The glue will hold down the laminate layer in normal use, but that alone won't stop it from splitting apart if the cutter pushes it away. Regard the join between layers as if it were like wood grain and use a backup where needed.
Manmade composites generally have even density and no grain to splinter, which makes them popular for routing. Unfortunately, they are so abrasive that tools get used up fast. Have a spare flush trim bit available when you really need it. Wherever you can't afford the risk of chip-out spoiling laminate, switch to a fresh one for the final pass.
Pressure
Do not press too hard against the template. Take several strokes to work in gradually. Aggressive passes in hardwood are more difficult than in softwood. If you're getting ready to use a large profile bit, rough out the shape with other tools first. On the last pass, engage the full profile lightly.
Heavy pressure can momentarily slow the speed of a weak motor. At the moment it slows, gouging is likely. If you can hear it struggling, that's a good clue the bit is over the hill. If you've been using the same one a long time, it gets less able to cut without gouging.
Feed rate and tearout
A slow rate makes a neater cut. On a scrap of the same material, practice even, steady stroking until your cuts stop tearing out. Hard, dense oak lumber is cut at a slower speed than soft, porous materials. There are exceptions. Solid surface is very dense. Paradoxically, slow feed can make it bumpy. It's not exactly tearing; flakes of plastic adhere to it.
Router bit flutes
The number of flutes varies on different kinds of router bits. A single flute feeds fast but may tend to cut rougher than two straight flutes. A straight flute is common, but it is not the only kind. Shear flutes lean a little.
If a pilot isn't needed, consider solid carbide spiral bits. A slow spiral bit has curved edges that twist around in a helix. Spirals have a modest capacity. While an upcut spiral twist bit lifts waste up and out, it may promote chipping on the top of LPL. A downcut spiral is pressing in and avoiding top splintering. To preserve both faces of melamine laminate, try a compression spiral bit. It has opposing spirals to shear both ways simultaneously. This style is more costly.
Vibration and runout
Steady a panel that is rocking or bouncing. Intricate shapes such as stile and rail may be improved by clamping over the standard fence a custom-made fence that matches the shape closely. This fence can be homemade to come very near to the bit and extend as far as neeeded. Use a bandsaw to rough out the middle of the cutout to clear the top of the cutter. Secure it then advance until a precise cutout straddles the bit and only the profile protrudes.
Router bits shouldn't vibrate noisily; they should hum. Vibration causes tearout to worsen. Running the motor faster may magnify it. If it does not improve, blow out the debris and try remounting it. If a wide profile vibrates excessively, it might be due to weight imbalance. A tall bit tends to bounce and flex near the tip, so choose one no longer than necessary.
Router bit tearout and noise may be a sign it's wearing unevenly or out of round. A routed groove with a width greater than the width of a bit that made it may be evidence of runout. Only occasionally can you correct it by remounting it in a different orientation. Make inspection with a dial indicator to see if it is within a hair or .003 in. Touching up the flute profiles can worsen runout.