The gears are critical to the comfort and ease of ride of the bike, and I chose mine with care. I use 21 speed Shimano gears, and look after them carefully. Keeping the chain, driving members and gear changers clean and well-lubricated is essential to continued trouble-free operation. I use gears mostly from the Acera X range, with Shimano IG chain. Although pretty much entry level in the Shimano range, this equipment has performed well in the field. I've had a couple of snapped chains, but those were overdue for a change... largely the gear set has been trouble free throughout the life of the bike. Whenever the chain is changed, the rear cassette (the block of 7 gears on the rear sprocket) is changed also to ensure a good fit.
The crank-ring gear changer has traditionally proved to be the most troublesome and tricky to set up. Whilst simple in function, I still have a little trouble adjusting the changer to operate faultlessly from the lowest, hill climbing ring to the centre, everyday ring, and obtaining the correct adjustment to avoid the chain catching noisily on the changer in extremely high gears can be only a little short of impossible. It's normally pretty OK when it comes back from services, but cable stretch plays havoc with the positioning over time.
The rear gear changer has never really given me any bother at all; short of having a couple wear out they seem to function well. A little adjustment of cable tension, and cleaning the crud off the jockey wheels is all that seems to be required. I'm actually amazed at the resilience of the system... due to the position it's not hard to knock the changer about on low obstacles, get it tangled up with undergrowth, brambles an so forth, but usually a quick clearing of the debris gets it functioning well again.
The gear selectors are fantastic. Now in common usage, I'd never seen them before when I bought the bike. To move up a gear, one pulls the top trigger towards you, and to move down, one pushes the bottom trigger away. The move and engage with a positive action and give a nice tactile feedback in use.
To lubricate the chain, I generally use a dry lubricant such as Ice Wax. Wet lubricants tend to attract grit and dirt... and every month or so I degrease the chain and gears and re-lubricate them.