You can use pyspark.sql.functions.lead() and pyspark.sql.functions.lag() but first  you need a way to order your rows. If you don't already have a column that determines the order, you can create one using pyspark.sql.functions.monotonically_increasing_id()
Then use this in conjunction with a Window function.
For example, if you had the following DataFrame df:
df.show()
#+---+---+---+---+
#|  a|  b|  c|  d|
#+---+---+---+---+
#|  1|  0|  1|  0|
#|  0|  0|  1|  1|
#|  0|  1|  0|  1|
#+---+---+---+---+
You could do:
from pyspark.sql import Window
import pyspark.sql.functions as f
cols = df.columns
df = df.withColumn("id", f.monotonically_increasing_id())
df.select(
    "*", 
    *([f.lag(f.col(c),default=0).over(Window.orderBy("id")).alias("prev_"+c) for c in cols] + 
      [f.lead(f.col(c),default=0).over(Window.orderBy("id")).alias("next_"+c) for c in cols])
).drop("id").show()
#+---+---+---+---+------+------+------+------+------+------+------+------+
#|  a|  b|  c|  d|prev_a|prev_b|prev_c|prev_d|next_a|next_b|next_c|next_d|
#+---+---+---+---+------+------+------+------+------+------+------+------+
#|  1|  0|  1|  0|     0|     0|     0|     0|     0|     0|     1|     1|
#|  0|  0|  1|  1|     1|     0|     1|     0|     0|     1|     0|     1|
#|  0|  1|  0|  1|     0|     0|     1|     1|     0|     0|     0|     0|
#+---+---+---+---+------+------+------+------+------+------+------+------+