I have ethernet connection and its connected to a router and then to my computer using the LAN port of the router . Everything is fine but the router is kept on another floor and thus , I cannot use wifi on other devices as I get very weak signal . So , my question is that if I buy another router and connect it with my first router and finally connect my computer with the second router , will this affect my internet speed ?
If the two routers are connected through cable the answer is almost no (you pay a little overhead).
But you don't need another router, an access point (or a repeater) is a better choice.
Note: you must choose a different non-overlapping wireless channel for the 2nd router. http://en.wikipedia.org/wiki/List_of_WLAN_channels
Yes it can slightly affect the speed and also it will do 2x NAT translation which can make issues, so this is not recommended.
What you need to buy is a wireless access-point (AP), which doesn't have a router function (or it can be disabled). You just connect the AP to your router via cable as another computer and it will create a wifi network for you.