Site visited recently (April, 2018). It is one of those places that are easier to visit with an organised tour than alone mostly due to cost reason.
Several tour agencies in Saint Louis organise daily tours to Djoudj Reserve. Prices are around 30.000 CFA per person for the group of minimum 4 tourists. The trip usually takes half a day starting around 8.00 am and finishing aproximately at 15.00 - 16.00. To have a better understanding - CFA has mostly fixed rate to Euro (655 CFA, it was the same when being in 2014 in Burkina Faso)
If want to visit the place independently (which I did) you shoul be prepared for some huge costs. First of all is transportation - as it is around 60 km from Saint Louis town (25 km is a good asphalted road, while the rest is on dirt, local, not necessarily 4x4). The costs for this part (including waiting time in the park) is 25.000 CFA (unfortunately this amount is stated in Lonely Planet guidebook as an indicator, so it is quite difficult to negotiate the price but anyway try). At the park entrance you have official state prices for everything: guide (obligatory, although only French speaking) 6.000 CFA per group, boat trip 4.000 CFA per group, entrance fee per person 5.000 CFA, entrance fee for the car 10.000 CFA. So as you see depending on the number of people the trip may be somehow expensive. To reduce costs a little bit you can skip the boat trip and go for walking in the park but that is not recommended as the boat trip is the most interesting part of park visiting.
The most important areas are those at the end of boat trip where the majority of migrating birds are located. View of thousands of pelicans, herons, egrets, cormorants is truelly amazing. Acording to guide's information the best time to visit the park is winter (December to March) and the beginning of spring (until May) - while the birds are staying there.
Comparing all UNESCO Heritage Sites in Senegal I found Djoudj as one of the most interesting mainly due to the large number of birds (and other mammals - warthogs, monkeys) and relatively less rubbish (especially in relation to Saint Louis island).