Choose dwarf or determinate varieties for a bucket
A 10 litre (2.6 US gal) reservoir with one 10 cm (3.9 in) net pot cannot support a full indeterminate vine. Those varieties grow to two metres (6.6 ft), set fruit along the whole stem over months, and need root volume the bucket does not have. They are not impossible, but they become a full-time job of pruning and support, and yield per litre is poor.
Choose one of: determinate (bush) varieties, which grow to a set height, fruit once over a short window and then stop; dwarf indeterminates bread specifically for containers; and micro-dwarf types for a windowsill, which stay under 40 cm (16 in). The variety list on this site carries days-to-harvest and height for each entry — sort by height before anything else.
Light is the main determinant of yield
Of everything in this guide, this is the part worth reading twice. Tomato fruit set and sugar accumulation are close to linear with the light the plant receives. A windowsill gives you a healthy plant with a handful of fruit; that same plant under 12 hours of decent supplemental light will give you several times as much.
If you are growing for a kitchen supply rather than curiosity, budget for light before you budget for anything else.
Reservoir and feeding
Transplant into the net pot once the seedling has its first true leaves and roots are showing. Hold EC around 1.4 for the first fortnight while the root system establishes, then raise to 1.8–2.2 through flowering and fruiting. pH 5.8–6.2 suits the plant well.
By the time the plant is fruiting it will be consuming a lot of water. Measure the EC daily if you can: falling EC means the plant is eating faster than drinking, which is fine; rising EC means it is drinking faster than eating, and you should top up with plain water rather than more nutrient. In warm weather a mature plant may need a litre or more a day added.
Change the reservoir at least every fortnight once fruiting begins. The plant's nutrient demand shifts as fruit matures and a reservoir left too long goes out of balance in ways no pH adjustment will fix.
Pollination, and why flowers drop
Tomato flowers are self-pollinating — the pollen is inside the same flower — but they need vibration for the pollen to fall onto the stigma. Outdoors, wind and bumblebees do this. Indoors, nothing does. Give the flower truss a flick with a finger every day or two at midday, or use an electric toothbrush held against the stem behind the flowers.
If flowers open and then drop without setting fruit, the usual cause is temperature rather than pollination. Above about 30 °C (86 °F), or below 15 °C (59 °F), pollen becomes non-viable. This is the classic reason a healthy-looking plant sets nothing for a fortnight in a heatwave.
Pruning and support
Pinch out side shoots that appear in the angle between a branch and the main stem if you are growing a cordon type — they divert energy and make the plant unmanageable. For determinate and dwarf varieties, leave them; they are what produce the crop.
Remove the lowest leaves once the plant is a foot tall. They touch the lid, stay wet, and are the first thing to go mouldy. Keep a fan moving air around the plant.
Every tomato plant needs something to lean on. A single stake through the net pot to 1.2 m (3.9 ft) is enough for a dwarf; a cordon will need string to a fixing above.
The failure to expect first
Blossom end rot. A black, sunken patch at the bottom of the fruit — the end furthest from the stem. Like lettuce tipburn it is a calcium distribution failure, not a shortage. The causes are uneven watering, high EC, and rapid growth after a dry spell.
Fix: keep the reservoir level stable, lower EC slightly, and stop swinging the water temperature. Removing the affected fruit is worthwhile — they will not recover — and the plant's later fruit is usually fine. Do not add calcium supplements to the reservoir expecting a fix; the plants are almost always calcium-replete already.