Randogne is on the 422 bus line between Sierre (20 mins., CHF 9.80) and Crans Montana (10 mins., CHF 5.20). There is a stop on the funicular railway in the neighbouring village of Bluche but it's quite a hike.
A vehicle would be quite useful. There are also many hiking trails in Randogne and the surrounding area. Most are well-marked. A map can be purchased at the Tourism Office in Crans Montana for CHF 5.00.
Randogne's main attraction is undoubtedly the Déchetterie de Comogne, about 40 minutes walk out of the centre of the village: take the route du Pafouer to the Ferme des Trontières (stop to take a look at the unique cheese vending machine), then take a left along the Allée Elisée Bonvin (signposted "Déchetterie") until you reach the village dump. That's the Déchetterie.
Have a picnic at the wonderful municipal picnic site located just next to the Déchetterie.
There are no shops in Randogne. There is a Raiffeisen Bank branch equipped with an ATM, which is helpful since the branch is only open between 9:00 am and 11:00 am on Wednesdays.
Eat and drink
is for wuzzes.
The [Montana] resort is not very far away up the mountain, but most of the trip is practically vertical, so it can be a bit challenging to get there if you are not in shape. There are many hiking trails in and around Randogne that will take you up there. Otherwise, there is an intermittent bus service (CHF 5.20) that will take you up, or you can take the funicular up after hiking over to Bluche or down to St-Maurice-de-Lacs. If you travel down to Sierre, either by bus or funicular, you can visit the Wine Museum and the Rainer Maria Rilke Foundation.