I am an ophthalmology resident, so I have some knowledge in this area. I am still in training and am not a retina specialist so take what I say with a grain of salt.
The "floaters" you described are a posterior vitreous detachment(PVD), caused by breakdown and liquefying of the vitreous, a gel-like substance which fills the posterior segment of the eye. These are extremely common and while annoying, don't require any treatment. While the floaters may seem like a major problem if you haven't had to deal with them before, I would recommend giving it some time. Generally the floaters will settle at the bottom of the eye, and eventually your brain will learn to ignore and "see around" the floaters to some degree, making them less noticeable. Someone earlier in the thread mentioned laser and surgery as options for getting rid of the floaters, but I would recommend extreme caution before proceeding with either of the two options.
There is a doctor in Florida who advocates treating PVD with the Nd:YAG laser. Zapping the PVD with a laser won't actually get rid of a PVD, it will just break it up. Now instead of a large floater, you'll have multiple smaller floaters which may or may not be an improvement. Safety-wise, the incidence of retinal detachment associated with the YAG is close to 0, however, the laser is typically used to treat parts of the eye more anterior and usually requiring few shots. Trying to vaporize a floater would require the laser to be directed more posterior which would require more energy and more shots to be effective. The YAG works by creating a small shockwave inside the eye which is not something I would want close to the retina. I'm not aware of any studies looking at incidence of retinal detachment following YAG laser treatment of PVD, but I would imagine from a physiologic standpoint that it would be higher. My opinion is that laser treatment for floaters is of questionable efficacy with an increased risk of retinal detachment.
There are some retina doctors who perform pars plana vitrectomy for patients with floaters. However, while generally considered a "safe" surgery, there is about a 2% risk of retinal detachment, 1% risk of secondary cataract formation intraoperatively, overall increased risk of cataract formation postoperatively, and <1% risk of endophthalmitis, infection inside the eye. Someone stated above that these are "low." It may seem so looking at the numbers, but in your case this would be an elective surgery. A retinal detachment is a major complication. While it can be repaired, the eventual visual outcome is variable depending on the circumstances. If the detachment does not involve the macula, the area of the retina responsible for your central vision, in many cases vision can be restored to 20/20 - 20/40. Some patients only regain 20/50-20/200 vision. A small amount of patients are only able to visualize hand motions or can only perceive light. The outcomes are even worse for RD that do involve the macula. The surgery itself can also either cause cataract or accelerate cataract formation which can require an additional surgery to address. And while the chances of it occurring are very low, getting an infection inside the eye can be catastrophic, oftentimes resulting in severe visual impairment even with appropriate treatment. Any time you perform intraocular surgery you run this risk. LASIK or PRK only address the cornea, the front of the eye which means that getting an infection is much milder and is limited only to the ocular surface. Other complications of vitrectomy are macular edema or epiretinal membrane which can affect your vision just as badly and possibly more noticeably the floaters.
Vitrectomy overall is considered a low risk surgery, but generally that is in the case of a patient with a retinal detachment who runs the risk of losing vision without the surgery. In your case where you are likely 20/20 with a condition that has a benign course, the risks generally outweight the benefits unless you are experiencing severe visual debilitation as a results of the floaters.
The tldr version: Don't get the laser or the surgery unless the floaters are bothersome to the point where your activities of daily living and quality of life are severely impaired.
My public service announcement: If you suddenly experience a new floater associated with any of the below symptoms:
1)flashing lights
2)a shower of many floaters, i.e. 50-100
3)a dark curtain dropping over your vision
Although the risk is generally low, these symptoms in the context of a new floater can signal a retinal tear or detachment and you should be seen by an ophthalmologist as soon as possible.