Guide to improving your mobile phone connection
Ranked in increasing cost and difficulty

Action or Technology

Benefits

Limitations

Research before purchase: Read reviews before purchasing your next phone. Look for phones with the best antenna performance - Price or manufacturer has no bearing on this. 
A good antenna design uses less power and retains a more robust connection.
Will help to make sure you get the best available performance in areas of poor signal coverage. Does not indicate how the phone will perform where you need/want to use it.
Sweet Spot: Move around all rooms in turn and check the vertical bar graph icon of mobile signal strength. If you have a few friends over, why not take the opportunity to compare phone signals and between different service providers. 
Key requirements: A mobile phone which signal meter or a 'Cell Network' App.
Easy to check where the best signal reception is located. You could use a bluetooth headset or headphones to allow use whilst moving around the same room when on a call. You need to use the phone in the same location to help prevent disconnections. 
Reflectors: You can make up a curved board lined with tin foil to act as a directional reflector. The phone is held at the focal point in front of the reflector. This helps to direct the transmission both to and from the 'cell' tower. Finding out the direction to the nearest mobile 'cell' may help but sometimes the signal quality does not rely just on distance. Some modern houses feature foil backed insulation in walls (particularly bathrooms) which will act to reflect your phone signal. You may be able to determine this from finding your sweet spot.
Key requirements: Cardboard or thin board, tin-foil, glue.
Easy and cheap to make. More precise parabolic dishes are harder to construct but provide much better performance. Improves mobile data rates. You could also use a bluetooth headset for ease of use. Best if combined with the sweet spot method. Have to fix in one position. Need to know the rough direction of cell tower but the best position for the reflector can be checked by trial & error using signal strength indication on the phone.
Wi-Fi calling: Some providers can allow your mobile to use your broadband routers Wi-Fi connection to connect telephone calls via the internet. This service is subject to your standard mobile call charges and call allowance and additionally your home broadband data allowance.
Key requirements: Standard domestic broadband connection and WiFi router.

 

Good connection and reliable as long as the your ADSL broadband service and WiFi router are working OK.  Reliant on the Wi-Fi signal quality around the home. Have to pay for both the phone and internet usage. Also needs good broadband speed.
3G/4G Router: Creates a 3G signal with in your property - For example - Vodafone Sure Signal. Uses both your home broadband and mobile data allowance - You will need to switch off mobile data on the phone and use the WiFi data connection to prevent the use of your mobile data allowance.
Key requirements:  you'll need a phone that's on the same network and a standard domestic broadband connection download speed of 2 Mbps. 
Purchased direct from your network provider. Easy DIY installation. Fits into a plug socket. Connection settings can be changed using your online network account. Only phones that are manually registered can connect to the unit (upto 32 phones), 8 devices can connect at once with a broadband download speed of 4.13Mbps. Limited range. Only works at your registered homes IP address (cannot move between properties).
Although it works with the majority of broadband providers and most routers, not all are compatible. Does not work with satellite broadband, WiMax, bonded lines, or secure firewalls. 
Phone signal booster: They receive your phones signal and boost it to the cell tower and at the same time receive the signal from the cell and boost it to your phone (sometimes called a repeater). These units are either externally fixed to the wall or utilise an external directional antenna. Uses mobile data allowance.
Key requirements: Best with externally fitted antenna.
Can provide a very good and reliable mobile signal. Best option for overall mobile service use within the whole property.  Expensive, can be difficult to fit and may require an AC power supply to the unit (a UPS can keep the unit powered in case of mains outages). Some models may need some technical configuration to setup. Legal versions limited to specific networks.
What if there is no mobile signal and I only have no/slow broadband?: 1. Your remote property could be in a valley or in the signal shadow of a hill or large building. If it is only you and there is a property nearby that can receive a mobile signal you could consider asking them to host a phone signal booster with two directional external antennas, one facing you and the other facing the cell.
2. If there a number of you with the same issue you could consider crowd funding a 'femto cell' from a specific network who will install a 'small' cell in the shadow zone this could be combined with a microwave link that is able to provide a faster broadband service. 
The first option would typically cost the same as fitting the booster unit described above. The second option will provide a mobile service just as good as within many other towns. First option requires a friendly and willing neighbour for the installation site. Care needs to be taken on installation requirements to ensure adequate service. The second option is very expensive and requires network approval so is only viable if many homes are willing to either push or pay for the improved service.