Why do I have slow internet speed with my NETGEAR WNDR4300v2 wireless router

The short answer is that the speeds you are getting may already be close to the best you can achieve.

It is important to understand the difference between link speed and throughput.  Link speed is the physical rate at which all bits are sent.  This includes both the overhead bits used for synchronization, error correction, etc. as well as bits for the payload (e.g. bits that are part of a video stream, web page, file, etc.).  Throughput is the rate at which payload bits are sent.  When you run an Internet speed test, you are actually measuring throughput.  

In case it's not obvious, throughput is always less than link speed.  For some physical media, like Ethernet, cable or DSL, link speed and throughput differ by only a few percent.  The kicker is that, for Wi-Fi, throughput can be 50% or lower than the link speed.  A helpful rule of thumb is to take the link speed and cut it in half to get an approximate, maximum, useful throughput.

But it gets worse.  Other factors can cause the actual link speed to drop.  These include radio interference from other Wi-Fi networks; noise sources like baby monitors, microwave ovens and cordless telephones; signal loss due to absorption/reflection by walls; and a drop in signal strength due to distance.  In addition, Wi-Fi standards require that devices operating at 2.4 GHz to use narrower, 20 MHz channels instead of 40 MHz channels.  As you can imagine, with all other factors being equal, the link speed of a 20 MHz channel is half as fast as a 40 MHz channel.  At 5 GHz, 40 MHz channels are very common.  Routers that support newer Wi-Fi protocols, like 802.11ac, can even use 80 MHz and 160 MHz channels.

So, let's take a router, like your WNDR4300v2.  300 Mbps is the maximum achievable link speed on a 40 MHz channel using 802.11n Wi-Fi protocols.  Using what I said previously, you can expect throughput up to around 150 Mbps.  Your measured throughput of 117 Mbps while using the 5 GHz network likely reflects the fact that your actual link speed was less than 300 Mbps.  On a Windows machine, you can see the link speed by looking at the Wireless status of the Wi-Fi adapter.  On a Mac, click the Wi-Fi icon while holding down the option key to see the link speed.

Your throughput at 2.4 GHz is even lower because the router is probably restricting itself to using a 20 MHz channel.  Hence, the link speed is 150 Mbps or less, with expected throughput half of that, or 75 Mbps or less.  You measured 55 Mbps, so this is in the ball park.

So, is there anything you can do to increase these speeds?  There are a couple of settings you can try.  Both of them are under the Advanced Wireless Settings on the router.  The first is to set the Preamble mode to short.  This forces the router to use fewer overhead bits for data synchronization.  Under good conditions, this may increase speeds by a small percentage (likely <10%).  Under bad, it may make things worse, so measure throughput with it on and off.  The second is to disable 20/40 MHz Coexistence.  This setting only applies to the 2.4 GHz network.  Disabling this setting encourages the router to use 40 MHz channels.  The caveat is that this requires the cooperation of devices.  Some devices, like Apple iPhones and iPads, are notorious for refusing to use 40 MHz channels in the 2.4 GHz band.

Apart from that, there's not much else you can do other than to move the router and devices closer together and eliminate as much interference as possible.  Don't expect to get throughput anywhere near 300 Mbps.

[Edit: Oh, I forgot to mention that, because Wi-Fi is a two way street, that devices can also be the limiting factor.  Factors like the Wi-Fi protocol (802.11g, 802.11n, and 802.11ac), the channel width (20 MHz vs 40 Mhz) and the number of data streams can also affect speeds.  Using 802.11ac on both the device and router is usually the surest way to dramatically increase throughput.]