On foot
A fit traveler should be able to reach the village of Cully, in the center of the Lavaux from the port of Ouchy in Lausanne in about an two hours. If you're feeling more ambitious consider the popular walking tour of Lavaux vineyards. The whole walk from Chateau d'Ouchy Lausanne to Chateau de Chillion Montreux takes about 9 hours, not counting stops for wine-tasting and picnics. This should make for a relaxing 3-day itinerary if you book hotels at villages along the way. The Montreux-Vevey tourism board offers an excellent brochure with a detailed map of the entire bas-lavaux region called "A la découverte des terraces de Lavaux". It can be obtained upon arrival in Lausanne at the tourist office immediately outside the train station.
For no apparently good reason, it is much harder to find official guides detailing the footpaths and bike trails of Savigny and Forel, but the region is packed with gems for the discerning explorer, and is liberally peppered with charming, inexpensive places to stay. At least one web-site (http://www.welcome-lavaux...) provides an excellent source of attractive bed and breakfast accommodations throughout the entire Lavaux haut et bas, which are not to be found through the Montreux-Vevey tourist board's site (http://www.lavaux.com/).
By train
The regional trains stop at many of the villages along the way and can be used to get around (http://www.sbb.ch/en/). However, the Lausanne-Montreux line runs close to the bottom of the Lavaux, near the big lake, so you are guaranteed to see almost nothing on the train ride except gorgeous views of LacLéman and the Savoie Alps between Lutry and Vevey, and the train stations are often in the suburban commerce centers of the larger municipalities, away from the vineyards themselves. There is also a Train-des-Vignes that runs from Vevey to Puidoux which can be quite scenic if you aren't fit enough to hike or walk around the Lavaux. There is also a funicular from Vevey to Mont-Pelerin station where you can walk in perhaps 1.5 hours to the Mont-Pelerin summit at 1080 m which has a viewing tower, a train from Vevey to Les Pleiades 1360 m, and several others. Although not exactly the Lavaux, the cogwheel train from Montreux to Rochers-de-Naye 2042 m is great because of excellent views on a clear day although slightly expensive.
By bus
Regular buses No. 65 service run 7 days a week from the Lausanne Metro stop "La Sallaz" to the Lavaux's high altitude communes of Savigny and Forel. These two villages make ideal starting points for countryside walks, or family cycle trips on quiet lanes. cycle transport is permitted on the buses, and for the adventurous but lazy, electric cycles can be rented in Forel.
On Bicycle
Cyclists with strong legs and a decent bicycle may find the Lavaux to be a great place to cycle some hills, and the entire Lausanne-Montreux stretch is easily doable in anywhere from under 2 hours if you take the uninteresting path the waterfront level or in a full day if you take the scenic and paved Route de la Corniche along the vineyards and make plenty of photo stops along the way. Be prepared to walk your bicycle on some roads that are too steep, test your brakes very well, and watch out for extremely steep sections of roads around the corner when descending along vineyard routes. Cycles could be rented in Lausanne for those without one in Switzerland. Get the brochure described above if you don't have a cycling map. For the more adventurous, why not also discover the Lavaux's hinterlands by pedalpower. An abundance of quiet well signed cyclable routes cover the unspoiled countryside between the Mont Pelerin above Chardonne and the communes of Puidoux, Forel and Savigny, from where you can freewheel all the way back down to the lakeshore at Lutry if your bike has reliable breaks.
If you are athletic, cycling is probably the best way to daytrip the bas-Lavaux because you will always be going right alongside the vineyards and villages rather than at the train stations below, and unlike driving, you can stop anywhere at ease to enjoy the breathtaking scenery. Start in Lausanne's waterfront at Ouchy, and simply hug the coast until you get to Lutry's old town; turn left, go uphill, and look for the Chateau de Bertholod sitting amongst vineyards. From there, simply follow a map, signs, or your desires eastward; it's hard to not reach Montreux because you will always have the giant lake in view to guide you. The Route de la Petite Corniche which later becomes the Route de la Corniche are particularly scenic. You can even stop in Chexbres for a budget lunch at the Coop, and then continue onwards. When you reach Montreux, catch an S train back to Lausanne with a bicycle ticket, or cycle back via the flat and fast roads at waterfront level.