Generate a list of random numbers and [`Accumulate`](https://reference.wolfram.com/language/ref/Accumulate.html):

 b = Accumulate @ RandomVariate[NormalDistribution[0, 1], 500];

 ListLinePlot[b, PlotRange -> 35]

[![enter image description here][1]][1]

For 2D, you can generate pairs of random numbers and `Accumulate`:

 SeedRandom[1]

 b2 = Accumulate @ RandomVariate[NormalDistribution[0, 1], {500, 2}];

 ListLinePlot[b2, AspectRatio -> Automatic]

[![enter image description here][2]][2]


 [1]: https://i.sstatic.net/A5xb8.png
 [2]: https://i.sstatic.net/RurhW.png