You could extend the existing fence posts upwards or insert new posts to bring your wallplate level to the height you need, say 2.5 metres.
Use 4x2" timber to form a wall plate and use same bolted to house as a ridge.
Form rafters, again using 4x2" at 400 or 600mm centres.
Get your roof material, I would recommend clear acrylic or polypropelene (same as conservatory roof except 1 or 2 skin, not 3) for your roof as relatively unbreakable but allowing natural light into store.
A length of gutter to control rain runoff and fit a side gate.
Use pressure treated timber throughout.
Depending on where you are you should have no problems getting this work done or handy for a good DIYer with tools