For wired solution,something like this(some modifications may be needed but overall basics are same):
How to use a spare router to make your home Wi-Fi better
For wireless solution,without sounding harsh but just give up.

I once tried it with 2 tplink wifi routers & barely manged to make it work with an unstable wifi connection & using same model wifi routers has the largest chances of working correctly in this setup compared to setup like yours which has very little chances of success.
That is also why it is recommended to get routers which support access point/AP mode or repeater mode. The other quick fix way is to get a repeater/extender as suggested.
Thanks a lot for your guidance!
Some Qs ..coz i would prefer not to spend again on repeater, but I am totally ok with it if required..As dilip said " you must understand that when you use a repeater, the speed becomes half. " Some scenarios:
1. Using my router dg-bg4300nu with dwr 113 d link as a repeater
with wire: how much loss (in % etc) happens?
2. Using my router dg-bg4300nu with a new repeater/extender: how much loss (in % etc) happens?
3. Buying a new router & using my dg-bg4300nu as an extender with wire: how much loss (in % etc) happens?
3. Buying a new router & using my dg-bg4300nu as an extender wireless: how much loss (in % etc) happens?
4. Any other option/combination?
What about switching it, that is using my dwr 113 d link as the main router & dg-bg4300nu as a repeater etc?
I know, too many questions but which would be the best option? (Also ,I really like to learn about several things & one of them is networking)
A bit confused about this-
"That is also why it is recommended to get routers which support access point/AP mode or repeater mode.
The other quick fix way is to get a repeater/extender as suggested." >> So, which is better? Replacing my router or extender?
Again, sorry for the many questions & thanks in advance!