One word: Friction!
During a winter of commuting in harsh cold weather, I re-discovered the beauty of friction shifters. I could never get my bike to shift too well with my RapidFire shifter because my shifter, cable and derailer were frozen and covered in snow. I recovered a dumpster bike with an old set of stem-mounted friction shifters. I took the shifters off, threw away the front shifter, and mounted it on the only tube that was the right diameter (my top tube), and I haven’t missed a shift since.
The first step is to find a shifter. Shifters should work with all cassettes and derailers although I have never tried it with a SRAM 1:1 derailer. Chances are you’re local bike shop will have a few kicking around that they’ll give you or sell you for under $5. Old garbaged 10 speeds are another great source. If you insist on putting something new on your bike, you can pick up something like this (note the list of compatibility, everything!) for $7.50. One note: if you find old 10 speed style shifters, make sure you get the clamp as well. If they mount direct to the downtube you may need to keep searching unless you have downtube mounts on your own bike.
The second step, install it. Start by removing your old shifters, saving the old cable and housing if you can/desire. Find a spot to mount your new find, remembering it doesn’t necessarily need to be on the handlebar. Run the cable and housing as you normally would, and I recommend liberal use of lube so as to keep down the maintenance. Some even go so far as to pack a bit of grease in each end of the housing to create a seal that will keep some of the road grime out and the lube in. Make sure your derailer limit screws are adjusted properly (they should be if you are simply removing your old shifter), ensure the shifter is in the position with the most slack (when you pull the shifter, it pulls cable, not releases it). Pedal the drivetrain to move the chain to the smallest cog, and then tighten the cable down in the derailleur. If you experience a bit of a dead spot in the shifter, i.e. the first few degrees of activating it does not move the derailleur, you need to tighten the cable. You can either turn out the barrel adjuster or simply reattach the cable to the derailleur with a little more tension.
Friction shifters also have a friction adjuster. If the shifter is too hard to move by hand or if your shifts immediately slip back down, you need to adjust the friction. For more friction, screw the screw or knob in, and it should stop slipping. For less friction, unscrew the knob or screw, and the shifter should move a lot more easily.
If you have never used friction shifters or can’t remember the last time you did, you should find that shifting is easier than you think. I rarely have a problem with the chain not finding its gear. Even when shifting multiple gears at once, I’ll hit my gear 19 times out of 20. And even when my cable is frozen and gummed up with road grime or rusty from spending the night in the snow, I can always pull the cable through it to find the gear I need.