Nichrome wire not heating up with a 9v battery
A 9V battery is a poor choice for providing electrical energy for heating.
An Alkaline 9V battery can typically provide maybe a few watts of heat energy for a short while. 

If your wire resistance is too high the heat per wire length will be too low to notice.   

If your wire resistance is too low the battery will be excessively "loaded down" and will not deliver much heat energy. 

What is your application?



Given Nichrome wire:

42 gauge
Length = 1 inch
Using this calculator - link provided by Electronsurf.  

For temperature = 400 F / 204 C (coldest allowed by calculator) 

Wire resistance is : 5.8533 ohms
Power required = 0.33 watts.
REquired current = 0.24 A.
Required voltage = 1.4V

A 9V battery will be "loaded down" badly - it will try to supply
I=V/R = 9V / 6 Ohms = 1.5A.
or about 12 Watts.
This would be ample if the battery was able to maintain 9V.

A better match is a 1.5V Alkaline battery - AA or C or D (bigger the better)
Use copper wires  to extend the length of the wire. Nichrome wire does not solder well. You can clean the wire ends well with eg sandpaper and then twist copper wire around the ends. You MAY be able to solder this combination but with reasonably thick copper you can bend the wire over the joint and crimp it together. Adding a screw connector helps but in this case adds to the thermal mass and makes heating much harder. You can get fluxes that help soldering, but this should not be needed for experimenting. 



Is it really 42 gauge? - that is extremely thin. 

Again -  what is your application? knowing what you wan to achieve will help us help you. 

_______________________________________

9 Volt 'PP3' battery performance.

A 9V Alkaline battery may be capable of providing 1 few amps into a cl;ose to short circuit load - but this is abusing them to far beyond their specified ratings.

For an Alkaline 9V "PP3" battery  500 mA is typically the absolute maximum specified current. 

A typical "super heavy duty" 9V battery will output perhaps 1.5A on full short circuit fading approximately linearly to 300 mA in 40 S. Net Ah of battery under those conditions is about 10 - 20 mAh. [Ask me how I know :-) ].

As an indication of the upper end of specified performance of a PP3 battery - here is an Ultralife Lithium 9V battery with performance several times that of of a top alkaline.
It has a rated pulse discharge current of 1.05A,
has a continuous rated discharge current of 150 mA continuous (!)
and a protection PTC rated at 700 mA. 

Here is an Energiser Alkaline PP3 rated at 500 mA max continuous discharge.
SC MAY be several amps - for under a minute.