Without an explicit example it is hard to give you some insight in to data cleaning. However, there are common functions that are used to select/convert/transform data:

Part (* to select parts of something based on indices *)
Select (* to select something base on a True/False criterion *)
Cases/FirstCase (* to 'select' something based on its structure *)
ToExpression (* to convert a string to an expression *)
UnitConvert/Quantity/QuantityMagnitude (* to add/remove/convert quantities *)
StringSplit (* split string-data in to parts*)
StringTake/StringDrop (* take parts of strings *)
Map/Apply (* used in conjunction with ToExpression, to convert an entire bunch of items to expression *)
Delete (* delete based on indices *)
DeleteCases (* delete based on a pattern-match *)
DeleteDuplicates(By) (* delete duplicates*)
ArrayReshape/Flatten/Partition/Transpose/Reverse (* flipping/flattening/changing dimensions et cetera*)
Replace/ReplaceAll/StringReplace (* replace items based on replacement rules *)

I think with those, you can get quite far. Of course then you can 'group' the data using:

Gather/GatherBy/GroupBy
Split/SplitBy

Or count items:

Tally/Count/Counts/CountsBy

Sort items:

Sort/SortBy

Then you can do some statistics on it to reduce the data:

Min
Max
Mean/TrimmedMean/Total
Median
StandardDeviation/Variance/RootMeanSquare
Skewness
Kurtosis
Length

Summarization of data

Some time ago I programmed a function, RecordsSummary, inspired by R's summary. Here is an example of its usage: Census data summary .

As the name implies, it is assumed that we have a list of records, all with the same length, and we want the columns to be summarized. (Each record is a row.)

You can get the package MathematicaForPredictionUtilities.m from MathematicaForPrediction at GitHub or simply run this command:

Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/MathematicaForPredictionUtilities.m"]

Let us create random data.

data = RandomInteger[{0, 100}, 100];
dataCat = RandomChoice[Characters["azbuka"], 100];
data2 = RandomInteger[{0, 100}, {100, 4}];

Here are examples of using RecordsSummary over the created data.

1. Call on a 1D array:

RecordsSummary[ data ]

2. Summary of a 2D numeric array. The columns are named automatically.

RecordsSummary[N[data2]]

3. Fancy output of numerical and categorical data summary. The column names are the second argument given to RecordsSummary.

Grid[{RecordsSummary[
   Transpose[{N[data], dataCat}], {"Numeric", "Categorical"}]}, 
 Alignment -> Top, Dividers -> All]

Mosaic plots

Using Mosaic plots for data exploration/visualization was described in these WordPress blog posts and this Community discussion.

Here is an example:

Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/MosaicPlot.m"]

titanicDataset = Map[Flatten, List @@@ ExampleData[{"MachineLearning", "Titanic"}, "Data"]];
Dimensions[titanicDataset]
(* {1309, 4} *)

titanicVarNames = Flatten[List @@ ExampleData[{"MachineLearning", "Titanic"}, "VariableDescriptions"]]
(* {"passenger class", "passenger age", "passenger sex", "passenger survival"} *)

MosaicPlot[titanicDataset[[All, {1, 3, 4}]], ColorRules -> {3 -> ColorData[7, "ColorList"]}]