Computers are wonderful, but they have screwed up the younger generations' notion of high fidelity reproduction. With this question, we have a person utterly perplexed when presented with speakers that do not have a built-in amplifier.
You gave a model number for the speakers, but why no identification of the record player?
The nomenclature "record player" is usually reserved for self-contained units which have all the necessary electronics and speaker(s) all built into the same chassis. Because your unit has RCA cables for the signal output, we can safely assume it is not a record player, but rather a turntable.
What kind of cartridge is the turntable equipped with? The phono cartridge is a transducer -- it's a tiny electrical generator. It converts mechanical energy into electrical energy. In a ceramic cartridge, this is accomplished by the piezoelectric effect: stress on a crystal produces an electrical signal. Such a cartridge is fine if you're a six year old playing used records that were bought for 25 cents each.
If you're serious about playing records, then you'll want a moving magnet (MM) cartridge (there are other types such as moving coil and moving iron, but you don't need to concern yourself with them). The output signal from a MM cartridge is much weaker than the output from a CD player (or even a ceramic cartridge). Thus it requires a phono preamplifier to boost its signal up to line level. Additionally, when records are cut, low frequencies are cut (to reduce the area of the groove) and high frequencies are boosted (to overcome some inherent noise issues), so the phono preamplifier must undo this and apply the opposite equalization (i.e. it must boost the lows and cut the highs; ceramic cartridges achieve ). Modern cheap turntables may include a built-in phono preamplifier, in which case those RCA cables can be plugged into any line level inputs, otherwise they must be plugged into the phono inputs of a receiver (includes AM/FM tuner; preamplifier which provides volume/tone controls and switching functions; and lastly the power amplifier which boosts the signal to drive the speakers to the desired loudness), or integrated amplifier (just has power amp and preamp, no tuner). Not all integrated amps or receivers include a phono preamp (record playback fell out of popularity with the ascendency of the compact disc, but they are returning -- you can tell by checking if any inputs on the back of a given unit are labeled as "phono"). Of course separate phono preamps are available.
With compact discs, you just pop the disc in the player and push the play button. With records, you need to know how to align your cartridge, set tracking force, and how to keep the records clean. With the price of new vinyl, it doesn't make sense to "get into vinyl" unless you're prepared to invest in good equipment (which it doesn't seem you're at the point).