How do you build a small one room apartment to go in a backyard and what are the construction costs?

For the backyard, you can have your architect design the apartment space so that it fits within the backyard and conforms to the local authority requirements. If its in Nairobi, Kenya for example, it should conform to Nairobi city council building bye laws.
Your architect can advice on the best materials to use for the house. The house can be prefabricated in steel structure with SIP[structural insulated panel] infill or masonry walling. If is for rent, masonry walling is better since its long lasting and does not require regular maintenance. SIP steel structure has advantages in that its cheaper and faster to erect the house.

Online consultancy

You can email me the dimensions[length and width] of the backyard and a few digital images of the backyard. From here, i will design your apartment and email it to you or post it on www.prismafrica.blogspot.com for you to download.
Once you receive the house plans, you can then look for a builder near you to carry out the exact construction.
To add another extra room to your house, you will need to consult your architect to come up with house plans for the additional room. The additional room has to be planned such that it conforms to the local authority bye laws. In Nairobi, Kenya, it should conform to Nairobi city council bye laws.
You can email us the dimensions of the existing house, dimensions of the existing compound then we work on the design of the extension which we can post on our website www.prismafrica.blogspot.com for you to download.

Construction costs are estimated per square meter of built up area. The rate per square meter depends on the region that you intend to build. In Nairobi, Kenya for example, the rate is approximately KES 20,000 to 25,000 per square meter for a middle income class finish.
An average bedroom is 12m2 in area =12×20,000=KES 240,000-estimated cost of construction. Architect’s fees is 6% of the cost of construction.
Contact us for any further information.
www.prismafrica.blogspot.com