The secret to success with growing healthy plants in an aquarium is making sure the plants have everything they need. Just like plants in your garden, they need good lighting, regular fertiliser, carbon dioxide and something to grow their roots in. You don't need to splash out (!) on expensive tech - there are lots of ways to keep the costs down and still get great results.
Working from the bottom up, the base layer of your aquarium should at the very least be a good quality fine-grain gravel to allow easy root development and structure. Ideally you should add a fertiliser substrate layer under the gravel to give slow-release nutrients over several years, but you can always cheat and target-feed plants with fertiliser balls later on. If you want to go the whole hog you can have under-gravel heating to make more constant and efficient use of the fertiliser layer.
Is a CO2 Kit essential?
Aquatic plants need Carbon Dioxide (CO2) dissolved in the water to grow and thrive. In the wild, CO2 is constantly produced when mud and detritus at the bottom of lakes and rivers is broken down by bacteria. In an aquarium there is not enough naturally occurring CO2 to sustain healthy plant growth. Your tap water has been thoroughly aerated when you ran it from the tap and then by your aquarium filter, and is so saturated with oxygen even before it enters your tank that it can't carry much CO2. Adding a CO2 kit allows you to inject measured doses of CO2 into the aquarium to give plants optimum growing conditions and prevent algae growth. If you aren't ready for a kit yet, you can still get great results with Liquid Carbon - even the little £4.99 bottle treats 5000 litres!
How do I add fertiliser?
Fertilisers can be liquids added to the water or tablets poked into the gravel directly under the roots. Tablets are best for slow-growing deep-rooted plants, and usually last 6 months or more. Liquid fertilisers are best for the faster-growing stem plants and can be added daily or weekly - the important thing is to add them on a regular schedule so you get steady, even growth rather than stumpy plants with odd lanky sections because you only remembered to glug some fertiliser in twice a month!
What lighting is best?
This is hard to cover in a nutshell, but in general a bright warm light for abut 8 hours a day gives the best results. This can be the 'sunlight' effect tubes or 'plant lights' or the RGB LED lights which have a high concentration of red and green light to stimulate plant growth. Avoid blue lights for freshwater as they don't give enough for good plant growth and tend to cause algae.