I'll try to field your questions in the order that makes the most sense to me:
Would I have to write a bootloader and record it manually on theexternal flash or can I just use the internal bootloader, and somehow map it to the external devices?
You will have to write your own bootloader for this part. The bootloader will have to read the program stored on the flash (likely using SPI) and load it to your external RAM. A good description is given in this application note:
AN10835 - LPC2000 secondary bootloader for code update using IAP
Is it only necessary to connect it via hardware and put LOW or HIGH on
some pins on boot for the microcontroller to recognize those external
resources as its own, or will I also have to do something else?
In order to use external SDRAM you will have to properly configure and initialize
the external memory controller on the device. This includes configuring the pins on that part for their alternate functions.
For this, I'd recommend studying the chapters on pin configuration and the external memory controller in the LPC2294 user manual carefully. Then I would suggest get an eval board that comes with demo code for setting up the external memory controller and initialization code for the SDRAM on the eval board. A quick google search turned this eval board up:LPC-L2294-1MB(www.olimex.com/Products/ARM/NXP/LPC-L2294-1MB/), which also has some bootloader code. You can probably find others.
Once you feel you understand what the EMC and SDRAM initialization code are doing, you can think about selecting select a different SDRAM for your application. You should be able to read through the data-sheet and figure out what modifications you need to make to the initialization code from that point. Unfortunately, setting up the EMC for external SDRAM for the first time is non-trivial compared to some other peripheral setups. I would suggest you make use of the resources and forums at LPCWare (www.lpcware.com) to aid in your efforts.
What I want to do is connect those ICs to the microcontroller in order to expand its Program memory and data memory automatically (which means that I don't want to have to create a method to write on the flash or SDRAM, I want the microcontroller to be able to tell that it has those resources, and use them as if they were the microcontroller's on chip memories).
As I mentioned, for the FLASH, you're probably stuck implementing a custom bootloader as described in the AppNote. In the case of SDRAM, there will be a memory range extending from some base address defined for external SDRAM. Effectively, the microcontroller knows to use the external memory controller when it executes instructions that access those addresses, so it's fairly seamless during application development once it's set up. To get a better understanding of how the external memory controller works with dynamic memory I strongly suggest you also read the technical documentation provided by ARM: ARM PrimeCell™ MultiPort Memory Controller (PL176) Technical Reference Manual