Without more information my advice would to definitely install drainage. If you have nowhere to drain TO, you can easily create a 'dry well', a pit lined with LS fabric, filled with drain rock, covered with fabric and then covered with gravel, more drain rock or cobble...the trench would be landscape fabric, perforated pipe wrapped in landscape fabric then backfill the trench with drain rock, then landscape fabric, then soil or mulch or sod. Keep the soil thick enough to support your sod so it doesn't dry out faster than the rest of your grass.
Get rid of some of your mucky soil to allow a bed of 4" of crushed gravel. Install 2X4 edging with stakes, line the bottom with landscape fabric then install your 4" crushed gravel (3/8 minus if you can find this smaller size rather than 5/8 minus). For a professional touch, rent a compactor and compact your gravel.