You can set it up as a wireless access point to increase your range, however this requires an Ethernet connection between the two routers and some configuration.
It's not a good idea to use multiple routers unless you turn off the routing functions and use them as wireless access points. Your wireless signals will interfere with each other if they're operating on the same wireless channel. A router also acts as a DHCP server to assign IP addresses, you only want one DHCP service running.
Dynamic Host Configuration Protocol (DHCP) is an auto configuration protocol used on IP networks. DHCP allows a computer to be configured automatically, eliminating the need for intervention by a network administrator. It also provides a central database for keeping track of computers that have been connected to the network. This prevents two computers from accidentally being configured with the same IP address. http://en.wikipedia.org/wiki/Dynamic_Host_Configuration_Protocol
You'll need to manually configure the additional router before placing it into service. The IP address needs to be changed so it doesn't conflict with the first router, the DHCP functions should also be disabled on the second routers.
You'll have to connect a PC or laptop directly to the Lynksys WRT150N via Ethernet and log into it's interface to change it's IP. You'll want to change this to something that doesn't conflict with the first router but is in the same subnet.
Plug a Ethernet cable from the first router into one of the LAN ports on the second router, Don't use the second router's WAN port for anything.
Also use non overlapping wireless channels such as 1, 6, 11. You can use the same SSID for everything.
For example if you main router has an IP of 192.168.1.1 and it broadcasts on channel 1
Set your second router as an access point with an IP of 192.168.1.2 and have it broadcast on channel 6
That being said,
No router or combination of routers will change your Internet speed.
Your Internet speed is determined by your ISP and is measured in Mbps (Millions of bits per second). You can test your Internet speed here: http://speedtest.net
For example, If you have a 3 Mbps Internet connection, the maximum shared Internet bandwidth available to all of the devices connected to the router(s) will be 3 Mbps.
This connection bandwidth is shared among all of the users of your LAN. So any bandwidth others are using will be deducted from the total WAN (Internet) bandwidth that is available to you.
If you have a 3 Mbps Internet connection and one user is utilizing 2.5 Mbps of the bandwidth to download a file or stream a Netflix movie, that only leaves 0.5 Mbps for all of the rest of the users on the LAN.
In simple terms, the more users you have the more speed will be required. Streaming video, such as Netflix and Hulu require a lot of bandwidth. Here are the minimum recommendations from Netflix. https://support.netflix.com/en/node/306
Many people would be likely be surprised at how many active connections their wireless router has. I have dozens. cell phones, tablets, iPods, game consoles, laptops, desktops, ROKU boxes, Internet enabled devices such as TVs and audio receivers, and the list goes on.
Fast wireless routers and connections are designed to stream large files on your LAN quickly. The high speed routers permit fast transfer of files between devices connected to your LAN, however WAN speed is still limited by your ISP. The only way to Improve your Internet speed is to upgrade your plan or switch to a faster ISP.
Good Luck...