"Tedd" empowered us with this mighty blow against the
Patriarchy:

i have two tanks that are about to finish their nitrogen cycles, now i
have high nitrates. i have a few plants (two types) but i have no idea
what they are, i had got them because 1.) i heard they would help with
the cycling and 2.) to give the fish something to nibble on.

Just be warned that some LFSes will sell you terrestrial plants which may
look good for a while but will not last long under water.

Plants do consume some nitrogen-cycle products, but you should verify that
your ammonia and nitrites should cycle down to zero before adding fish.

nitrite .25 ppm
nitrate 80-160 ppm

Your nitrite level is a bigger problem than your nitrate level. Nitrites
(and ammonia) should be zero, otherwise your tank hasn't finished cycling
yet.

20 gal (US):
ammonia 0 ppm
nitrite .25 ppm
nitrate 40 ppm

Ditto.

the plants i have in there now *seem* to be doing fine, (they are
growing) one is a floating viney type plant with a multitude of blade
type leaves that come directly off the stem, each plant is a single
stem that has grown to about 12-14 inches (36-40 cm) with 3 stems
floating in each tank.

Possibly hygrophilia polysperma, which is an excellent plant for a new tank
as it's a fast grower.

what is the best "beginners" plants to have and where should i read up
for more information,

http://faq.thekrib.com/plant.html

http://faq.thekrib.com/plant-list.html

and what is the best way to control nitrogen
levels.

Once your tank has cycled, ammonia and nitrites will be processed into
nitrates by your biofilter, unless you overload your tank:

http://faq.thekrib.com/begin-cycling.html

Plants will consume some nitrates but typically nitrates are removed via
water changes, which you should be doing anyway. It's ideal to keep
nitrates below 40ppm, though most fish will tolerate higher levels.