How do I wire up this item (BM70 - Microchip BTLE) for prototyping
This board is designed as a daughterboard, to be soldered from both sides to a larger PCB. But it's possible for a hobbyist to prototype with it. Every hobbyist eventually learns the limitations of breadboards: as simple as they are, there are times when they simply won't do the job. There are mainly two possibilities.

First of all, don't care how ugly the construction is, the first goal is to make it work. A prototype is subjected to numerous changes on-the-fly anyway.

Use a Perfboard

A perfboard is a single or double-sided empty circuit board with a matrix of holes. There are no connections on the board, and one is free to solder the board in all possible ways. Although it's not designed for SMT, it's certainly can be done.

An extreme example is shown here.


Source: @Philips_NE555 on Twitter, fair use

You can either choose to assemble the entire circuit on a perfboard, or you can cut a small piece of perfboard, buy a row of standard 2.54mm connectors, and solder your module on the perfboard. Once assembled, you can hook up wires, just like a standalone module. 

I recommend:


If you don't have any experience with perfboards, purchase some cheap electronic devices (like a 555 timer in surface mount package) and build some circuits for practice. Also, once the circuit works, try desoldering every single component from your board without damage (if inexperienced, a lot of damage can be created in this process). Particularly, a double-sided board is sometimes challenging to desolder, those plated through-holes can be nasty, and need practice. I recommend a single-sided perfboard, although you cannot solder from both sides, it's easier to (re)work with.
Use AWG-30 wirewrap wire or magnetic wire for interconnection.
Important: Solder some 0.1 uF ceramic decoupling capacitors across the power and ground on the perfboard. Solder some electrolytic (100 uF or so) filter capacitors. It ensures the power integrity of the daughterboard. Also, keep all signal wires as short as possible. 


More information:


Wikipedia: Perfboard


Dead-bug Construction

In a dead-bug construction, a bare copper board is used. The chip is flipped to its back, with leads and wirings hanging in the free-air. Sometimes, tapes are used to stop the chip from touching the copper board. 

A dead-bug construction is essential for high-frequency digital electronics and radio electronics, as it provides a continuous ground plane as a low-impedance return path. 

However, it seems that your BM70 module is already a self-contained module, and it's not mandatory to use a copper board, but you may find it useful. 

 
Source: IEEE Spetrcum, fair use

More information:


Hackaday: Getting Ugly, Dead Bugs, And Going To Manhattan
IEEE Spectrum: With the “Dead Bug” Method, Hobbyists Can Break Through the High-Frequency Barrier


Homebrew PCB, or Design and Buy a PCB

It depends on the circumstance, but sometimes a homebrew PCB is an easier plan to execute than a prototype board, a lot of wiring time can be saved. 

If you are not sure about the circuit, you don't have to design a PCB that contains the full circuit, it can just be a breakout board: a row of connectors, a bunch of traces, and a row of pad for soldering the module. 

This is a computer system I was building at home.



There are various resources online for homebrewing PCBs, just search it. The photoresist process is the most common. But you need some tools.


Buy UV-sensitive prototype circuit boards, these boards are just regular copper boards with a layer of UV-sensitive chemical (cheap). Buy chemicals (cheap). Buy some plastic containers (cheap). Buy etchant (an acidic solution, cheap). Buy safety goggles (cheap). Buy a set of PCB drill bits (cheap) Buy a blacklight UV-exposure box (30-50 USD). Buy a drill press (the most expensive part, a cheap model can do the job, if you are just making a single, drilling the holes manually might work as well). 
Design your PCB in a CAD package on a computer, as usual, but single-layer.
Print out the layout on a film, using a printer. 
Put the film on the board, expose board under UV light.
Put the board in a exposure solution, the covered portion remains, but the uncovered portion is washed away, leaving a layer of exposed copper. Put the board in the acidic solution, the copper dissolves in the solution, forming the circuit pattern. 
Drill.
Solder.


More Information:


How to Make a Printed Circuit Board (PCB) Using the UV Light LED Method.


Design your PCB, and Send it to a Factory

Alternatively, if you don't want to make PCBs at home, you can design your own PCB and outsource it to a manufacturer. There are plenty of manufacturers from China that take orders online, you can tell a factory to make a board for you in a few mouse clicks. And it can be as cheap as 10 dollars. 

The disadvantage is time. You'll need to wait for 3-5 days, but you can have professional-quality boards. A faster order from a local business (e.g. OSH Park in the USA) is possible, but makes it more expensive.

More Information


How to Order Cheap Custom PCB Online