Hi Christine,
OK, the basic things you need for plant growing are good light (buy one of the fluorescent tubes designated as suitable for growing plants) and fine grade gravel or if you don't want substrate in your tank, then pots to grow the plants in with some pebbles to hold them in the pots. Don't use sand as it compacts too much and can result in areas of toxic anerobic bacteria building up. I find that about two inches depth of substrate is fine for growing most plants - more then deep enough to bury their roots. You can get away with less however as long as you don't put massive plants in the tank.
If you have reasonable levels of nitrates and phosphates in your tank then you don't need to buy extra fertiliser (mine do very well with just the fish's natural wastes to feed on), but if you really want to go in for some serious aquaculture then you'd lay down a layer of sand with warming tubes underneath, then a layer of fertiliser and finally a top layer of substrate, and add a CO2 device or liquid CO2. Most of the hardier varities will do fine without all this though.
As for choosing plants, you need to find the varieties that are:
1) suitable for the light level you have. Most will do fine if you have a good fluorescent tube designed for plants but some - like Red Cabomba - need really intense lighting.
2) suitable for cold water. Plants have a preferred growing temp, so check which ones will grow in cold water. Some are only for tropical tanks.
3) suitable for the pH and hardness of your water; some like soft acid water and others aren't fussed what they live in. Most prefer a neutral pH.
3) distasteful to goldfish! Unfortunately, GF do eat plants so you'll need to experiment with different varietiies to find out what they won't eat. Mine won't eat Java Fern, cryptocorynes, spiky grasses or green Cabomba (unless they're feeling really hungry). They do seem to love purple or red coloured plants though.
Some good basic candidates for a GF tank with reasonable light and neutral-ish pH are: Java Fern (which needs its rhizome tied down to rocks or wood, not buried in the substrate), Amazon Sword, Hornwort, Elodea, most of the Cryptocoryne family, straight or spiral Vallisneria, Green Cabomba, any of the spiky grasses, Anacharis and Anubia.
When you buy plants, choose a couple of tall varieties for the back, some medium height ones for mid-range and some smaller ones for the front. Choose an odd number rather than an even number for a more natural effect and try to intersperse them with your ornaments - rocks or driftwood or whatever - as this looks more natural too.
When you get them, they'll either come in with their roots in plastic baskets filled with rock wool or with sponge wrapped round and tied with lead. Remove all of these things first before putting them in the tank (especially the lead). Gently separate out the roots then push them into the substrate or pots, whichever you prefer, taking care not to break the roots. It's best to sort of sweep them in sideways rather than push straight down. Smooth the gravel around their bases so they are firmly anchored (or pile on pebbles if in pots) .... et voila!
Hope this helps.
