Indoor plants live under genuinely different conditions to anything growing in a garden bed, and most of the common problems people run into come down to a handful of basics rather than anything mysterious.
Light is the first thing to get right, and most popular houseplants actually want bright, indirect light rather than either deep shade or full, direct sun. A spot a metre or two back from a window, or beside one that doesn't get hours of direct sun through the glass, suits the majority of common houseplants well. Direct sun magnified through window glass can scorch leaves, showing up as pale, bleached or crisp brown patches on the side of the plant facing the window, which is often mistaken for disease or a watering problem when it's really a light problem.
Overwatering is the single most common way people kill a houseplant, by a wide margin. It's an easy mistake to make because watering on a fixed schedule, every few days regardless of conditions, feels like responsible care, but most houseplants would rather dry out slightly between waterings than sit permanently damp. Waterlogged roots can't take up oxygen properly and eventually rot, and by the time a plant's leaves show the damage, yellowing, wilting despite wet soil, the root damage is often already done. Checking the soil before watering, a finger a few centimetres down, and only watering when it's actually dry at that depth rather than on autopilot, is the single biggest habit change that saves the most houseplants.
Overwatering is the single most common way people kill a houseplant, by a wide margin.
New Zealand homes create a specific seasonal problem worth knowing about: winter heating dries the air indoors considerably, and many popular houseplants originate in naturally humid environments and can show stress, crisping leaf tips and edges in particular, when heated indoor air is much drier than what they'd get outdoors or in a greenhouse. Grouping humidity-loving plants together, standing pots on a tray of damp pebbles, or a simple room humidifier all help offset the drying effect of a heated NZ living room over winter.
Repotting is worth doing when a plant actually shows you it needs it, rather than on a fixed schedule. The two clearest signs are roots visibly circling round and round the inside of the pot when you slide the plant out, and roots growing out through the drainage holes at the base. Both mean the plant has outgrown its current container and its roots have nowhere further to go, and it's time to move up to a pot one size larger rather than waiting for growth to stall completely.