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To build an arched garden bridge is not so complex if the span is kept reasonable and strength can be achieved using two 2x10s or 2x12s to make the span.
Once the length is determined you will need four frame members of the sizes you choose. Two will be for the walkway and two will be for the hand rails, cut using the same router and pendulum method I describe in the bridge plan PDF on this site under free pdf's.
Secure your frame member perpendicular to an 8 foot long work bench or screwed together frame on horses sturdy enough to brace the frame member and to attach a router to a fulcrom and pendulum at the other end.
A powerful plunge cutting router is than adjusted to the arch that is most pleasing being sure not to cut away too much wood at the height/depth of the arch. You will see that you are simultaneously cutting the top and underside of the arch so split your material equally for strength so that when completed the bottom of the arch keeps three inches of material to the board edge.
When both pieces are cut out secure the bottom piece which is now the top hump of the arch to the upper part of the 2x10 that has become the bottom of the arch using glue, screws and especially bolts on larger bridges. You can see what I mean on the pdf that shows the three steps of assembly.
Hand rails are made using the same router and pendulum technique and spacing each cut about three inches apart to retain the same arch as the bridge so the hand rails will match perfectly. All other supports and parts can usually be taken from the scrap pieces if you were careful with your planning and cutting.
Deck the frame members with what ever 5/4 decking is suitable for your plan making them about 2-3 feet wide is general acceptable with a two arch frame. If a wider bridge is decided upon then add a third arch down the center of the span to prevent deck sagging.
Remember these bridges are cosmetic and delicate and intended for garden foot traffic only. Consult an engineer if you are planning to build a bridge for commercial use.