If you share a kichen and are not able to control the cooking habits of others, it is helpful to occasionally pour a pan of boiling water down the drain to help remove the beginnings of a grease plug.
Once a drain has stopped, try a small rubber plunger. They are cheap and effective at freeing vegetable matter caused backups. CAUTION: if the drain pipes are corroded and old, and especially if they are leaky, efforts to unplug with a plunger or any pressure generating or mechanical snaking device is likely to burst the corroded pipe and dump a sink-worth of filthy water at your feet and on downstairs neighbors. This is why the plumbing intervention is listed first.
Never put large amounts of vegetable peelings or seeds in a garbage disposal. The result is almost certainly going to be an intractable plug. Better to compost anyway.
If you've done all the above, there's little harm that will come from an occasional shot of sodium hydroxide solution to remove fatty or hair deposits. A properly installed and used drain should only need this treatment rarely. Buy it in a small container and "use to completion" so you won't have a bottle sitting around where children can be accidentally exposed.
Bathroom drain plugs are usually hair related. Even with a drain sieve in place, some will slip by and snag around the in-pipe stopper. It's really not so hard to remove the internal drain device and clean it with rag. Gross yes. Hard no. If that's not going to be an option for you, a caustic cleaner is one of the few remaining options.
After years of use a bathtub or shower drain becomes narrowed with condensed soap scum and disgusting hard water precipitates. The narrowing makes for easier plugging. Caustic cleaners will not touch that problem. Enzyme powders can be purchased for this purpose. Be patient. Follow the directions and it will likely reduce the freqency of clogging.
Another common cause of clogging is the intrusion of tree root tips into the discharge line that carries wastewater from your home and into the sewer beneath the street. When that happens, ground-level sinks and toilets slow, with the lowest ones backing up first. Caustic drain cleaners will not touch tree roots. You can buy a bottle of cupric sulfate crystalls to flush down the toilet: that will usually kill the roots off in short order. Or you can hire the "rooter man" to have at it with an electric cutter head on a cable. Ultimately, the root intrusion problem calls for replacement of the connector line.