All of the following is given on the links and references pages but it seems useful to duplicate the information on a separate how-to page.
The state-of-the-art (in early 2023)
The design space occupied by human powered aircraft is large enough for there to be no single 'state of the art.' If you mean long range then Daedalus and many of the Japanese aircraft flying in the Annual Birdman Cup are state of the art. If you mean slower and lighter than Gossamer Albatross is still the state of the art. If you mean 'high' speed, 'practical', and manoeuvrable then Musculair, Aerocycle, and some of the Team-F aircraft are state of the art. And scattered among all of these aircraft are design details that are state of the art.
That stated the the DMG MORI Birdman House IGA aircraft represents (in my opinion) the present state of the art.
Details of the DMG MORI Birdman House IGA aircraft and its construction are here - HIGHLY RECOMMENDED
The development and construction of Aerocycle, John Edgely, RAeS, 2017 download (87 MB file)
Long Builds & Short Flights, My Experience of Flying and Constructing Human Powered Aircraft, Kit Buchanan, RAeS, 2022 download (20 MB file)
Inflatable Structures and their Application to Human Powered Flight, F. To, RAeS, 2010 download
Aluminium and wire-braced structures - MIT Monarch and Gossamer Condor
J. S. Langford, "A Human Powered Speed Aircraft With Electrical Energy Storage," MIT S. M. Thesis, May 1984. Download here is a really useful detailed case study for the design of an HPA. It includes all of the calculations for the design of an HPA and some of the code (In BASIC) that was used. It is recommended as essential reading.
Gossamer Condor plan set drawn by Paul MacCready download
Also, refer to the drawings on the download page these were drawn with the express intention that they should be useful to future builders and designers. Most of them were drawn full size from measurements of the aircraft or from the designer's drawings and then scaled down to fit on an A0 sheet, so they are accurate and can be imported into cad and scaled back up to full size and parts made, copied, or used to check calculations for new designs.
Details
How to make trailing edge download
Kit Buchanan's 3d printed propeller (in his RAeS lecture) download (20 MB file)
Gossamer Albatross construction - Pat Lloyds sketches - download
Airglow propeller construction download
How to make CFRP tubes download
Airglow seat download (Also Daedalus, Betterfly, and Aerocycle from a sketch by Mark Drela.)
Material and parts suppliers
Rohacell foam here
Easy composites - the site contains many good "how to" tutorials here
Arrow gears here
Davall gears here
TW metals - 6061-T6 aluminium aircraft tube here
Tools
Filament winding machine here
Advice
Try to go and see a successful HPA, it is by far the best way to understand how to put a light stiff strong structure together, failing that, refer to the drawings on this site and on several of the Japanese sites linked to on this site.
However good your design is it will only fly well if it is constructed to a high standard.
The author has now seen at least three aircraft built without any structure to carry in-plane loads in the wing with the result that the wing behaves like a wet noodle and the aircraft only flies briefly when the coupled in-plane and torsional defections accidentally get into balance for long enough for flight to be possible. Please refer to the drawings and or do the calculations and construct wings with the structure needed to carry in-plane and torsional loads. The MIT BURD's wings failed catastrophically on rotation because they contained no structure to carry in-plane loads.