You can do it with strtol, like this:

char *str = "ab234cid*(s349*(20kd", *p = str;
while (*p) { // While there are more characters to process...
    if ( isdigit(*p) || ( (*p=='-'||*p=='+') && isdigit(*(p+1)) )) {
        // Found a number
        long val = strtol(p, &p, 10); // Read number
        printf("%ld\n", val); // and print it.
    } else {
        // Otherwise, move on to the next character.
        p++;
    }
}

Link to ideone.

There are many ways to parse a string containing numbers. If you expect the string to have a fixed format with 2 integers, the simplest solution is to use sscanf():

#include <stdio.h>

int parse2numbers(const char *str) {
    int a, b;
    // sscanf returns the number of successful conversions
    int n = sscanf(str, "%d%d", &a, &b);

    if (n == 2) {
        printf("success: a=%d, b=%d\n", a, b);
        return 1;
    }
    if (n == 1) {
        printf("failure: only one number provided: a=%d, str=%s\n", a, str);
        return 0;
    }
    if (n == 0) {
        printf("failure: invalid format: %s\n", str);
        return 1;
    }
    printf("failure: encoding error: n=%d, str=%s\n", n, str);
    return 0;
}

If the string can contain a variable number of integers, you could use strtol() to parse one integer at a time:

#include <errno.h>
#include <stdio.h>
#include <stdlib.h>

void parse_numbers(const char *str) {
    long a;
    char *p;
    
    for (;; str = p) {
        errno = 0;
        // strtol returns a long int
        //        updates `p` to point after the number in the source string
        //        sets errno in case of overflow and returns the closest long int
        a = strtol(str, &p, 10);
        if (p == str)
            break;
        if (errno != 0) {
            printf("overflow detected: ");
        }
        printf("got %ld\n", a);
    }
    if (*str) {
        printf("extra characters: |%s|\n", str);
    }
}

Using sscanf and scansets the sub-strings can be extracted. The scanset %79[^:] will scan up to 79 characters that are not : and %79[0-9] will scan up to 79 characters that are digits. The %n specifier will capture the number of characters processed by the scan. This allow the sub-scans to start where the last scan left off.

#include <stdio.h>

int main ( void) {
    char a[80] = "";
    int c = 0;
    int result = 0;
    int each = 0;
    int span = 0;
    int offset = 0;
    char text[][80] = {
        "DATA:PHONENUMBER123456AGE7890"
        , "TEL:123"
        , "TEL1A:123456"
        , "TEL2B:123456"
    };

    while ( 1 == sscanf ( text[each], " %79[^:]:%n", a, &span)) {//scan up to : then scan :
        printf ( "\n%s\n", text[each]);//print full element of text array
        offset = span;
        printf ( "text before : = %s\n", a);
        do {
            if ( 1 == ( result = sscanf ( text[each] + offset, " %79[^0-9]%n", a, &span))) {// scan non-numbers
                offset += span;
                printf ( "\ttext = %s\n", a);
            }
            if ( 1 == ( result = sscanf ( text[each] + offset, " %79[0-9]%n", a, &span))) {//scan numbers
                offset += span;
                printf ( "\tnumber text = %s\n", a);
                if ( 1 == sscanf ( a, "%d", &c)) {//scan text number to int
                    printf ( "\tnumber value = %d\n", c);
                }
            }
        } while ( result != EOF);//loop until end of text[each]
        each++;//next element in text array
        if ( each >= 4) {
            break;
        }
    }
    return 0;
}

this should work :

#include <stdio.h>
#include <ctype.h>
#include <string.h>
#include <stdlib.h>

#define ML 81

char    *changeStr(char *str)
{
    char *new = NULL;;
    int i = 0;
    int length = 0;

    /* calulating the size to allocate with malloc for new */
    while (str[i])
    {
        if (str[i] >= 48 && str[i] <= 57)
            length++;
        i++;
    }

    /* if no numbers found, return new which is NULL */
    if (length == 0)
        return new;
    new = malloc(length * sizeof(char));
    i = 0;
    length = 0;

    /* filling new with numbers */
    while (str[i])
    {
        if (str[i] >= 48 && str[i] <= 57)
        {
            new[length] = str[i];
            length++;
        }
        i++;
    }
    new[length] = 0;
    return new;
}

/* I kept the functions you are using in the main, i would not
   use gets, but it's maybe easier for you to keep it */

int main()
{
    char str[ML]={0};
    char *New;

    printf("Enter string: \n");
    gets(str);
    New = changeStr(str);
    if(!New){
        printf("No changes in string.\n");
    }
    else
    {
        printf("Changed string:\n");
        printf("%s",New);
    }
    return 0;
}

You could try something like this:

• Walk the string until you find the first digit (use isdigit)
• Use strtoul to extract the number starting at that position
  • strtoul returns the number
  • the second argument (endptr) points to the next character in the string, following the extracted number
• Rinse, repeat

Alternatively you could tokenize the string (using "(,+)") and try to strtoul everything.

char date[]="20-02-2015";
int d,m,y;
sscanf(date,"%d-%d-%d",&d,&m,&y);

You can use strtok() to extract the two strings with space as an delimiter.

Online Demo:

    #include <stdio.h>
    #include <string.h>

    int main ()
    {
        char str[] =".Word 40";
        char * pch;
        printf ("Splitting string \"%s\" into tokens:\n",str);
        pch = strtok (str," ");
        while (pch != NULL)
        {
            printf ("%s\n",pch);
            pch = strtok (NULL, " ");
        }
        return 0;
    }

Output:

Splitting string ".Word 40" into tokens:
.Word
40

If you want the number 40 as a numeric value rather than a string then you can further use atoi() to convert it to a numeric value.

A combination of digit filtering and sscanf() should work.

int GetNumber(const char *str) {
  while (!(*str >= '0' && *str <= '9') && (*str != '-') && (*str != '+') && *str) str++;
  int number;
  if (sscanf(str, "%d", &number) == 1) {
    return number;
  }
  // No int found
  return -1; 
}

Additional work needed for numbers that overflow.

A slower, but pedantic method follows

int GetNumber2(const char *str) {
  while (*str) {
    int number;
    if (sscanf(str, "%d", &number) == 1) {
      return number;
    }
    str++;
  } 
  // No int found
  return -1; 
}

Yes you can do this easily with sscanf().

Following is an example. See it working here:

#include <stdio.h>

int main(void) {
    float a;
    int b;
    char *sNum = "43.533a,5532";

    sscanf(sNum, "%fa,%d", &a, &b);
    printf("a= %f || b= %d", a,b);

    return 0;
}

Output:

a= 43.533001 || b= 5532

Note: Since float is having precision to 6 decimal place by default, so you may need to consider it and correct it if necessary.

You can use the following algorithm:

• Initialise result to 0
• Iterate over characters of the string
  • If character is in the range ['0', '9'] then
    • Multiply the previous result with 10 (this is a decimal shift left)
    • Convert the character to the numeric value of the digit
    • Add the numeric value to the result

Bonus answer (I know OP removed [c++] tag): While the algorithm can be directly translated from natural language, it can be simplified in C++.

accumulate(begin(str), end(str), 0, {
    return isdigit(c)
        ? r*10 + (c - '0')
        : r;
});